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Searched refs:FresnelS (Results 1 – 25 of 79) sorted by relevance

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/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/SpecialFunctions/
H A DFresnelIntegralFunctions.m15 {FresnelS[b*x]^2/x^10, x, 0, Int[FresnelS[b*x]^2/x^10, x]}
17 {FresnelS[b*x]^2/x^8, x, 0, Int[FresnelS[b*x]^2/x^8, x]}
18 {FresnelS[b*x]^2/x^7, x, 0, Int[FresnelS[b*x]^2/x^7, x]}
19 {FresnelS[b*x]^2/x^6, x, 0, Int[FresnelS[b*x]^2/x^6, x]}
21 {FresnelS[b*x]^2/x^4, x, 0, Int[FresnelS[b*x]^2/x^4, x]}
22 {FresnelS[b*x]^2/x^3, x, 0, Int[FresnelS[b*x]^2/x^3, x]}
23 {FresnelS[b*x]^2/x^2, x, 0, Int[FresnelS[b*x]^2/x^2, x]}
24 {FresnelS[b*x]^2/x, x, 0, Int[FresnelS[b*x]^2/x, x]}
25 {FresnelS[b*x]^2, x, 4, (2*Cos[(1/2)*b^2*Pi*x^2]*FresnelS[b*x])/(b*Pi) + x*FresnelS[b*x]^2 - Fresne…
26 {x*FresnelS[b*x]^2, x, 0, Int[x*FresnelS[b*x]^2, x]}
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/SpecialFunctions/
H A DFresnelIntegralFunctions.m11 {FresnelS[a + b*x]/x, x, 0, Int[FresnelS[a + b*x]/x, x]}
18 {FresnelS[b*x]^2/x^10, x, 0, Int[FresnelS[b*x]^2/x^10, x]}
20 {FresnelS[b*x]^2/x^8, x, 0, Int[FresnelS[b*x]^2/x^8, x]}
21 {FresnelS[b*x]^2/x^7, x, 0, Int[FresnelS[b*x]^2/x^7, x]}
22 {FresnelS[b*x]^2/x^6, x, 0, Int[FresnelS[b*x]^2/x^6, x]}
24 {FresnelS[b*x]^2/x^4, x, 0, Int[FresnelS[b*x]^2/x^4, x]}
25 {FresnelS[b*x]^2/x^3, x, 0, Int[FresnelS[b*x]^2/x^3, x]}
26 {FresnelS[b*x]^2/x^2, x, 0, Int[FresnelS[b*x]^2/x^2, x]}
27 {FresnelS[b*x]^2/x, x, 0, Int[FresnelS[b*x]^2/x, x]}
28 {FresnelS[b*x]^2, x, 4, (2*Cos[(1/2)*b^2*Pi*x^2]*FresnelS[b*x])/(b*Pi) + x*FresnelS[b*x]^2 - Fresne…
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/SpecialFunctions/
H A DFresnelIntegralFunctions.m11 {FresnelS[a + b*x]/x, x, 0, Int[FresnelS[a + b*x]/x, x]}
18 {FresnelS[b*x]^2/x^10, x, 0, Int[FresnelS[b*x]^2/x^10, x]}
20 {FresnelS[b*x]^2/x^8, x, 0, Int[FresnelS[b*x]^2/x^8, x]}
21 {FresnelS[b*x]^2/x^7, x, 0, Int[FresnelS[b*x]^2/x^7, x]}
22 {FresnelS[b*x]^2/x^6, x, 0, Int[FresnelS[b*x]^2/x^6, x]}
24 {FresnelS[b*x]^2/x^4, x, 0, Int[FresnelS[b*x]^2/x^4, x]}
25 {FresnelS[b*x]^2/x^3, x, 0, Int[FresnelS[b*x]^2/x^3, x]}
26 {FresnelS[b*x]^2/x^2, x, 0, Int[FresnelS[b*x]^2/x^2, x]}
27 {FresnelS[b*x]^2/x, x, 0, Int[FresnelS[b*x]^2/x, x]}
28 {FresnelS[b*x]^2, x, 4, (2*Cos[(1/2)*b^2*Pi*x^2]*FresnelS[b*x])/(b*Pi) + x*FresnelS[b*x]^2 - Fresne…
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/mathematicatests/
H A DFresnelIntegralFunctions.m11 {FresnelS[a + b*x]/x, x, 0, Int[FresnelS[a + b*x]/x, x]}
18 {FresnelS[b*x]^2/x^10, x, 0, Int[FresnelS[b*x]^2/x^10, x]}
20 {FresnelS[b*x]^2/x^8, x, 0, Int[FresnelS[b*x]^2/x^8, x]}
21 {FresnelS[b*x]^2/x^7, x, 0, Int[FresnelS[b*x]^2/x^7, x]}
22 {FresnelS[b*x]^2/x^6, x, 0, Int[FresnelS[b*x]^2/x^6, x]}
24 {FresnelS[b*x]^2/x^4, x, 0, Int[FresnelS[b*x]^2/x^4, x]}
25 {FresnelS[b*x]^2/x^3, x, 0, Int[FresnelS[b*x]^2/x^3, x]}
26 {FresnelS[b*x]^2/x^2, x, 0, Int[FresnelS[b*x]^2/x^2, x]}
27 {FresnelS[b*x]^2/x, x, 0, Int[FresnelS[b*x]^2/x, x]}
28 {FresnelS[b*x]^2, x, 4, (2*Cos[(1/2)*b^2*Pi*x^2]*FresnelS[b*x])/(b*Pi) + x*FresnelS[b*x]^2 - Fresne…
[all …]
H A DInverseSineFunctions.m51 …rt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^5) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[Ar…
53 …1/3)*x^3*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^3) + (Sqrt[P…
55 {Sqrt[ArcSin[a*x]], x, 1, x*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])…
79 …3/Sqrt[ArcSin[a*x]], x, 7, -((Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^4)) + (Sqr…
81 {x/Sqrt[ArcSin[a*x]], x, 1, (Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(2*a^2)}
87 …i/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^5) + (3*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[…
89 …2])/(a*Sqrt[ArcSin[a*x]])) - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^3 + (Sqrt[(3*Pi…
91 {1/ArcSin[a*x]^(3/2), x, 2, -((2*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]])) - (2*Sqrt[2*Pi]*FresnelS…
97 …)/(3*Sqrt[ArcSin[a*x]]) + (4*Sqrt[2*Pi]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^4) - (4*Sqr…
176 {Sqrt[ArcSin[a + b*x]], x, 1, ((a + b*x)*Sqrt[ArcSin[a + b*x]])/b - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]…
[all …]
H A DCosineFunctions.m44 {Sqrt[x]*Cos[x], x, 3, (-Sqrt[Pi/2])*FresnelS[Sqrt[2/Pi]*Sqrt[x]] + Sqrt[x]*Sin[x]}
286 {Cos[1/4 + x + x^2]/x^2, x, 4, -(Cos[1/4 + x + x^2]/x) - Sqrt[2*Pi]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]] …
332 …Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] - (Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
334 {Cos[a + b*x^2]/x^2, x, 4, -(Cos[a + b*x^2]/x) - Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/…
341 …[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) - (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqr…
343 {Cos[a + b*x^2]^2/x^2, x, 5, -(Cos[a + b*x^2]^2/x) - Sqrt[b]*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*…
348 …x^2]^3, x, 10, -((3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(8*b^(3/2))) - (Sqrt[Pi/6]*C…
350 …t[6/Pi]*x])/(4*Sqrt[b]) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(4*Sqrt[b]) - (Sqrt…
352 …x) - (3/2)*Sqrt[b]*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] - (1/2)*Sqrt[b]*Sqrt[(3*Pi)/2]…
364 {Cos[a + b/x^2], x, 5, x*Cos[a + b/x^2] + Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x…
[all …]
H A DSineFunctions.m40 {Sin[x]/Sqrt[x], x, 2, Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[x]]}
274 {x*Sin[1/4 + x + x^2], x, 4, (-(1/2))*Cos[1/4 + x + x^2] - (1/2)*Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt…
275 {Sin[1/4 + x + x^2], x, 3, Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]]}
323 {Sin[a + b*x^2], x, 3, (Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] + (Sqrt[Pi/2]*Fre…
325 …]*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[b]*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
332 …[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) + (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqr…
339 …[6/Pi]*x])/(24*b^(3/2)) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(8*b^(3/2)) + (Sqrt…
341 …+ b*x^2]^3, x, 8, (3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(4*Sqrt[b]) - (Sqrt[Pi/6]*C…
343 …t[6/Pi]*x] - (3/2)*Sqrt[b]*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + (1/2)*Sqrt[b]*Sqrt[(…
357 …Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x] + Sqrt[b]*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/P…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/rubi-rules/SpecialFunctions/
H A DFresnelIntegralFunctions.m4 (*\[Integral]FresnelS[a+b x]^n \[DifferentialD]x*)
16 (*\[Integral]FresnelS[a+b x]\[DifferentialD]x \[LongRightArrow] (((a+b x) FresnelS[a+b x])/b)+Cos…
24 Int[FresnelS[a_.+b_.*x_],x_Symbol] :=
48 …tegral]FresnelS[a+b x]^2 \[DifferentialD]x \[LongRightArrow] (((a+b x) FresnelS[a+b x]^2)/b)-2\[…
56 Int[FresnelS[a_.+b_.*x_]^2,x_Symbol] :=
57 (a+b*x)*FresnelS[a+b*x]^2/b -
94 Int[x_^m_.*FresnelS[a_.+b_.*x_],x_Symbol] :=
95 x^(m+1)*FresnelS[a+b*x]/(m+1) -
124 …m FresnelS[b x]^2 \[DifferentialD]x \[LongRightArrow] ((x^(m+1) FresnelS[b x]^2)/(m+1))-(2 b)/(m…
132 Int[x_^m_*FresnelS[b_.*x_]^2,x_Symbol] :=
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/TrigFunctions/
H A D9.3 (d+e x)^m trig(a+b x+c x^2)^n.m17 {Sin[a + b*x + c*x^2], x, 3, (Sqrt[Pi/2]*Cos[a - b^2/(4*c)]*FresnelS[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi…
23 {Sin[a + b*x - c*x^2], x, 3, (Sqrt[Pi/2]*Cos[a + b^2/(4*c)]*FresnelS[(b - 2*c*x)/(Sqrt[c]*Sqrt[2*Pi…
27 …2] + (1/2)*Sqrt[Pi/2]*FresnelC[(1 + 2*x)/Sqrt[2*Pi]] + (1/4)*Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*…
28 {x*Sin[1/4 + x + x^2], x, 3, (-(1/2))*Cos[1/4 + x + x^2] - (1/2)*Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt…
29 {Sin[1/4 + x + x^2], x, 2, Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]]}
44 … x^3/6 - (1/16)*Sqrt[Pi]*FresnelC[(1 + 2*x)/Sqrt[Pi]] + (1/16)*Sqrt[Pi]*FresnelS[(1 + 2*x)/Sqrt[Pi…
48 {Sin[1/4 + x + x^2]^2/x^2, x, 5, -(1/(2*x)) + Cos[1/2 + 2*x + 2*x^2]/(2*x) + Sqrt[Pi]*FresnelS[(1 +…
77 …4*c)]*FresnelC[(b + 2*c*x)/(Sqrt[c]*Sqrt[2*Pi])])/Sqrt[c] - (Sqrt[Pi/2]*FresnelS[(b + 2*c*x)/(Sqrt…
87 …, 6, (1/4)*Sqrt[Pi/2]*FresnelC[(1 + 2*x)/Sqrt[2*Pi]] - (1/2)*Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*…
91 {Cos[1/4 + x + x^2]/x^2, x, 3, -(Cos[1/4 + x + x^2]/x) - Sqrt[2*Pi]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]] …
[all …]
H A D9.1 x^m trig(a+b x^n)^p.m59 {Sin[x]/Sqrt[x], x, 2, Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[x]]}
172 {x^0*Sin[a + b*x^2], x, 3, (Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] + (Sqrt[Pi/2]…
190 …+ b*x^2]^3, x, 8, (3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(4*Sqrt[b]) - (Sqrt[Pi/6]*C…
192 …t[6/Pi]*x] - (3/2)*Sqrt[b]*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + (1/2)*Sqrt[b]*Sqrt[(…
236 {Sin[a + b/x^2]/x^2, x, 4, -((Sqrt[Pi/2]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x])/Sqrt[b]) - (Sqrt[…
391 {x^(1/2)*Cos[x], x, 3, (-Sqrt[Pi/2])*FresnelS[Sqrt[2/Pi]*Sqrt[x]] + Sqrt[x]*Sin[x]}
393 {Cos[x]/x^(3/2), x, 3, -((2*Cos[x])/Sqrt[x]) - 2*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[x]]}
451 …Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] - (Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
469 …t[6/Pi]*x])/(4*Sqrt[b]) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(4*Sqrt[b]) - (Sqrt…
471 …x) - (3/2)*Sqrt[b]*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] - (1/2)*Sqrt[b]*Sqrt[(3*Pi)/2]…
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationRules/MathematicaNotebookFiles/SpecialFunctions/
H A DFresnelIntegralFunctions.nb27 RowBox[{"FresnelS", "[",
65 RowBox[{"FresnelS", "[",
75 RowBox[{"FresnelS", "[",
124 RowBox[{"FresnelS", "[",
135 RowBox[{"FresnelS", "[",
223 RowBox[{"FresnelS", "[",
250 RowBox[{"FresnelS", "[",
291 RowBox[{"FresnelS", "[",
399 RowBox[{"FresnelS", "[",
446 RowBox[{"FresnelS", "[",
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationTestHighlights/MathematicaNotebookFiles/
H A DErrorFunctions.nb1616 RowBox[{"FresnelS", "[",
1648 StyleBox["FresnelS",
1752 RowBox[{"FresnelS", "[",
1765 RowBox[{"FresnelS", "[",
1780 RowBox[{"FresnelS", "[",
1784 RowBox[{"FresnelS", "[",
2159 StyleBox["FresnelS",
2366 StyleBox["FresnelS",
2483 RowBox[{"FresnelS",
2518 RowBox[{"FresnelS",
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/InverseTrigFunctions/
H A DInverseSineFunctions.m51 …rt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^5) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[Ar…
53 …1/3)*x^3*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^3) + (Sqrt[P…
55 {Sqrt[ArcSin[a*x]], x, 1, x*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])…
79 …3/Sqrt[ArcSin[a*x]], x, 7, -((Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^4)) + (Sqr…
81 {x/Sqrt[ArcSin[a*x]], x, 1, (Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(2*a^2)}
87 …i/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^5) + (3*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[…
89 …2])/(a*Sqrt[ArcSin[a*x]])) - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^3 + (Sqrt[(3*Pi…
91 {1/ArcSin[a*x]^(3/2), x, 2, -((2*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]])) - (2*Sqrt[2*Pi]*FresnelS…
97 …)/(3*Sqrt[ArcSin[a*x]]) + (4*Sqrt[2*Pi]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^4) - (4*Sqr…
176 {Sqrt[ArcSin[a + b*x]], x, 1, ((a + b*x)*Sqrt[ArcSin[a + b*x]])/b - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]…
[all …]
H A DInverseCosineFunctions.m91 …a + b*x]])/(2*b)) + ((a + b*x)*ArcCos[a + b*x]^(3/2))/b + (3*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[A…
93 {1/Sqrt[ArcCos[a + b*x]], x, 1, -((Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/b)}
95 …b*x]^(3/2)) + (4*(a + b*x))/(3*b*Sqrt[ArcCos[a + b*x]]) + (4*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[A…
108 {1/Sqrt[a + b*ArcCos[c + d*x]], x, 6, -((Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos…
109 {1/Sqrt[a - b*ArcCos[c + d*x]], x, 6, -((Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a - b*ArcCos…
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/InverseTrigFunctions/
H A DInverseSineFunctions.m51 …rt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^5) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[Ar…
53 …1/3)*x^3*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^3) + (Sqrt[P…
55 {Sqrt[ArcSin[a*x]], x, 1, x*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])…
79 …3/Sqrt[ArcSin[a*x]], x, 7, -((Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^4)) + (Sqr…
81 {x/Sqrt[ArcSin[a*x]], x, 1, (Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(2*a^2)}
87 …i/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^5) + (3*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[…
89 …2])/(a*Sqrt[ArcSin[a*x]])) - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^3 + (Sqrt[(3*Pi…
91 {1/ArcSin[a*x]^(3/2), x, 2, -((2*Sqrt[1 - a^2*x^2])/(a*Sqrt[ArcSin[a*x]])) - (2*Sqrt[2*Pi]*FresnelS…
97 …)/(3*Sqrt[ArcSin[a*x]]) + (4*Sqrt[2*Pi]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^4) - (4*Sqr…
176 {Sqrt[ArcSin[a + b*x]], x, 1, ((a + b*x)*Sqrt[ArcSin[a + b*x]])/b - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/MiscellaneousFunctions/
H A DzTrigProblems.m67 {(Cos[x]*Sin[x])/Sqrt[x], x, 0, (1/2)*Sqrt[Pi]*FresnelS[(2*Sqrt[x])/Sqrt[Pi]]}
72 {x^2*Sin[a + b*x^2]^2, x, 7, x^3/6 + (Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqrt[Pi]])/(16*b^(3/…
74 …[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) + (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqr…
76 …x, 7, -(1/(2*x)) + Cos[2*a + 2*b*x^2]/(2*x) + Sqrt[b]*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*x)/Sqr…
81 …*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*Sqrt[x]] - 2*Sqrt[b]*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
82 …, -(1/Sqrt[x]) + Cos[2*a + 2*b*x]/Sqrt[x] + 2*Sqrt[b]*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*Sqrt[x…
83 …6/Pi]*Sqrt[x]] - 3*Sqrt[b]*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*Sqrt[x]]*Sin[a] + Sqrt[b]*Sqrt[(…
84 …qrt[x]) - Sqrt[b]*Sqrt[Pi/2]*Cos[4*a]*FresnelS[2*Sqrt[b]*Sqrt[2/Pi]*Sqrt[x]] + 2*Sqrt[b]*Sqrt[Pi]*…
87 {Cos[a+b*x]/x^(3/2), x, 5, -((2*Cos[a + b*x])/Sqrt[x]) - 2*Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[…
89 …rt[x]) - 3*Sqrt[b]*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*Sqrt[x]] - Sqrt[b]*Sqrt[(3*Pi)/2]…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests4/InverseTrigFunctions/
H A DInverseSineFunctions.m134 …rt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^5) + (Sqrt[Pi/6]*FresnelS[Sqrt[6/Pi]*Sqrt[Ar…
136 …1/3)*x^3*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(4*a^3) + (Sqrt[P…
138 {x^0*Sqrt[ArcSin[a*x]], x, 4, x*Sqrt[ArcSin[a*x]] - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x…
169 …3/Sqrt[ArcSin[a*x]], x, 5, -((Sqrt[Pi/2]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(8*a^4)) + (Sqr…
171 {x^1/Sqrt[ArcSin[a*x]], x, 3, (Sqrt[Pi]*FresnelS[(2*Sqrt[ArcSin[a*x]])/Sqrt[Pi]])/(2*a^2)}
179 …FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(16*a^7) + (9*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcS…
181 …i/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(2*a^5) + (3*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[…
183 …2])/(a*Sqrt[ArcSin[a*x]])) - (Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/a^3 + (Sqrt[(3*Pi…
192 …)/(3*Sqrt[ArcSin[a*x]]) + (4*Sqrt[2*Pi]*FresnelS[2*Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(3*a^4) - (4*Sqr…
201 …FresnelS[Sqrt[2/Pi]*Sqrt[ArcSin[a*x]]])/(15*a^5) - (5*Sqrt[(3*Pi)/2]*FresnelS[Sqrt[6/Pi]*Sqrt[ArcS…
[all …]
H A DInverseCosineFunctions.m113 …a + b*x]])/(2*b)) + ((a + b*x)*ArcCos[a + b*x]^(3/2))/b + (3*Sqrt[Pi/2]*FresnelS[Sqrt[2/Pi]*Sqrt[A…
115 {1/ArcCos[a + b*x]^(1/2), x, 3, -((Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[ArcCos[a + b*x]]])/b)}
117 …b*x]^(3/2)) + (4*(a + b*x))/(3*b*Sqrt[ArcCos[a + b*x]]) + (4*Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[A…
145 {1/Sqrt[a + b*ArcCos[c + d*x]], x, 6, -((Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a + b*ArcCos…
146 {1/Sqrt[a - b*ArcCos[c + d*x]], x, 6, -((Sqrt[2*Pi]*Cos[a/b]*FresnelS[(Sqrt[2/Pi]*Sqrt[a - b*ArcCos…
/dports/math/py-sympy/sympy-1.9/sympy/integrals/rubi/rubi_tests/tests/
H A Dtest_inverse_sine.py111 SplitSum, SubstFor, SubstForAux, FresnelS, FresnelC, Erfc, Erfi, Gamma,
210 …FresnelS(sqrt(S(10))*sqrt(S(1)/Pi)*sqrt(asin(a*x)))/(S(800)*a**S(5)) - sqrt(S(2))*sqrt(Pi)*Fresnel…
212 …x), x, -sqrt(S(2))*sqrt(Pi)*FresnelS(sqrt(S(2))*sqrt(S(1)/Pi)*sqrt(asin(a*x)))/(S(8)*a**S(3)) + sq…
214 …assert rubi_test(rubi_integrate(sqrt(asin(a*x)), x), x, -sqrt(S(2))*sqrt(Pi)*FresnelS(sqrt(S(2))*s…
229 …/sqrt(asin(a*x)), x), x, sqrt(Pi)*FresnelS(S(2)*sqrt(asin(a*x))/sqrt(Pi))/(S(4)*a**S(4)) - sqrt(S(…
231 …assert rubi_test(rubi_integrate(x/sqrt(asin(a*x)), x), x, sqrt(Pi)*FresnelS(S(2)*sqrt(asin(a*x))/s…
235 …FresnelS(sqrt(S(10))*sqrt(S(1)/Pi)*sqrt(asin(a*x)))/(S(32)*a**S(7)) + sqrt(S(14))*sqrt(Pi)*Fresnel…
237 …FresnelS(sqrt(S(10))*sqrt(S(1)/Pi)*sqrt(asin(a*x)))/(S(8)*a**S(5)) - sqrt(S(2))*sqrt(Pi)*FresnelS(…
239 …x), x, -sqrt(S(2))*sqrt(Pi)*FresnelS(sqrt(S(2))*sqrt(S(1)/Pi)*sqrt(asin(a*x)))/(S(2)*a**S(3)) + sq…
244 …S(5)/2), x), x, -S(4)*sqrt(Pi)*FresnelS(S(2)*sqrt(asin(a*x))/sqrt(Pi))/(S(3)*a**S(4)) + S(4)*sqrt(…
[all …]
/dports/math/reduce/Reduce-svn5758-src/packages/rubi_red/tests/TrigFunctions/
H A DCosineFunctions.m44 {Sqrt[x]*Cos[x], x, 3, (-Sqrt[Pi/2])*FresnelS[Sqrt[2/Pi]*Sqrt[x]] + Sqrt[x]*Sin[x]}
286 {Cos[1/4 + x + x^2]/x^2, x, 4, -(Cos[1/4 + x + x^2]/x) - Sqrt[2*Pi]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]] …
332 …Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] - (Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
334 {Cos[a + b*x^2]/x^2, x, 4, -(Cos[a + b*x^2]/x) - Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/…
341 …[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) - (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqr…
343 {Cos[a + b*x^2]^2/x^2, x, 5, -(Cos[a + b*x^2]^2/x) - Sqrt[b]*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*…
348 …x^2]^3, x, 10, -((3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(8*b^(3/2))) - (Sqrt[Pi/6]*C…
350 …t[6/Pi]*x])/(4*Sqrt[b]) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(4*Sqrt[b]) - (Sqrt…
352 …x) - (3/2)*Sqrt[b]*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] - (1/2)*Sqrt[b]*Sqrt[(3*Pi)/2]…
364 {Cos[a + b/x^2], x, 5, x*Cos[a + b/x^2] + Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x…
[all …]
H A DSineFunctions.m40 {Sin[x]/Sqrt[x], x, 2, Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[x]]}
274 {x*Sin[1/4 + x + x^2], x, 4, (-(1/2))*Cos[1/4 + x + x^2] - (1/2)*Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt…
275 {Sin[1/4 + x + x^2], x, 3, Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]]}
323 {Sin[a + b*x^2], x, 3, (Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] + (Sqrt[Pi/2]*Fre…
325 …]*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[b]*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
332 …[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) + (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqr…
339 …[6/Pi]*x])/(24*b^(3/2)) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(8*b^(3/2)) + (Sqrt…
341 …+ b*x^2]^3, x, 8, (3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(4*Sqrt[b]) - (Sqrt[Pi/6]*C…
343 …t[6/Pi]*x] - (3/2)*Sqrt[b]*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + (1/2)*Sqrt[b]*Sqrt[(…
357 …Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x] + Sqrt[b]*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/P…
[all …]
/dports/math/reduce/Reduce-svn5758-src/contrib/rubi-red/rubi4/IntegrationProblems/MathematicaSyntaxFiles/TrigFunctions/
H A DCosineFunctions.m44 {Sqrt[x]*Cos[x], x, 3, (-Sqrt[Pi/2])*FresnelS[Sqrt[2/Pi]*Sqrt[x]] + Sqrt[x]*Sin[x]}
286 {Cos[1/4 + x + x^2]/x^2, x, 4, -(Cos[1/4 + x + x^2]/x) - Sqrt[2*Pi]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]] …
332 …Sqrt[Pi/2]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] - (Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
334 {Cos[a + b*x^2]/x^2, x, 4, -(Cos[a + b*x^2]/x) - Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/…
341 …[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) - (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqr…
343 {Cos[a + b*x^2]^2/x^2, x, 5, -(Cos[a + b*x^2]^2/x) - Sqrt[b]*Sqrt[Pi]*Cos[2*a]*FresnelS[(2*Sqrt[b]*…
348 …x^2]^3, x, 10, -((3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(8*b^(3/2))) - (Sqrt[Pi/6]*C…
350 …t[6/Pi]*x])/(4*Sqrt[b]) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(4*Sqrt[b]) - (Sqrt…
352 …x) - (3/2)*Sqrt[b]*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x] - (1/2)*Sqrt[b]*Sqrt[(3*Pi)/2]…
364 {Cos[a + b/x^2], x, 5, x*Cos[a + b/x^2] + Sqrt[b]*Sqrt[2*Pi]*Cos[a]*FresnelS[(Sqrt[b]*Sqrt[2/Pi])/x…
[all …]
H A DSineFunctions.m40 {Sin[x]/Sqrt[x], x, 2, Sqrt[2*Pi]*FresnelS[Sqrt[2/Pi]*Sqrt[x]]}
274 {x*Sin[1/4 + x + x^2], x, 4, (-(1/2))*Cos[1/4 + x + x^2] - (1/2)*Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt…
275 {Sin[1/4 + x + x^2], x, 3, Sqrt[Pi/2]*FresnelS[(1 + 2*x)/Sqrt[2*Pi]]}
323 {Sin[a + b*x^2], x, 3, (Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/Sqrt[b] + (Sqrt[Pi/2]*Fre…
325 …]*Sqrt[2*Pi]*Cos[a]*FresnelC[Sqrt[b]*Sqrt[2/Pi]*x] - Sqrt[b]*Sqrt[2*Pi]*FresnelS[Sqrt[b]*Sqrt[2/Pi…
332 …[Pi]*Cos[2*a]*FresnelC[(2*Sqrt[b]*x)/Sqrt[Pi]])/(4*Sqrt[b]) + (Sqrt[Pi]*FresnelS[(2*Sqrt[b]*x)/Sqr…
339 …[6/Pi]*x])/(24*b^(3/2)) - (3*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a])/(8*b^(3/2)) + (Sqrt…
341 …+ b*x^2]^3, x, 8, (3*Sqrt[Pi/2]*Cos[a]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x])/(4*Sqrt[b]) - (Sqrt[Pi/6]*C…
343 …t[6/Pi]*x] - (3/2)*Sqrt[b]*Sqrt[Pi/2]*FresnelS[Sqrt[b]*Sqrt[2/Pi]*x]*Sin[a] + (1/2)*Sqrt[b]*Sqrt[(…
357 …Sqrt[2*Pi]*Cos[a]*FresnelC[(Sqrt[b]*Sqrt[2/Pi])/x] + Sqrt[b]*Sqrt[2*Pi]*FresnelS[(Sqrt[b]*Sqrt[2/P…
[all …]
/dports/math/py-mathics/Mathics3-2.2.0/mathics/builtin/specialfns/
H A Derf.py93 class FresnelS(_MPMathFunction): class
/dports/math/py-sympy/sympy-1.9/sympy/integrals/rubi/rules/
H A Dspecial_functions.py110 SplitSum, SubstFor, SubstForAux, FresnelS, FresnelC, Erfc, Erfi, Gamma,
232 …pattern6772 = Pattern(Integral(FresnelS(x_*WC('b', S(1)) + WC('a', S(0))), x_), cons2, cons3, cons…
238 pattern6774 = Pattern(Integral(FresnelS(x_*WC('b', S(1)))/x_, x_), cons3, cons3)
250 …pattern6778 = Pattern(Integral(FresnelS(x_*WC('b', S(1)) + WC('a', S(0)))**S(2), x_), cons2, cons3…
256 …pattern6780 = Pattern(Integral(x_**m_*FresnelS(x_*WC('b', S(1)))**S(2), x_), cons3, cons20, cons18…
262 …pattern6782 = Pattern(Integral(x_*FresnelS(x_*WC('b', S(1)))*sin(x_**S(2)*WC('c', S(1))), x_), con…
844 return Simp(cos(Pi*(a + b*x)**S(2)/S(2))/(Pi*b), x) + Simp((a + b*x)*FresnelS(a + b*x)/b, x)
868 …return -Dist(S(2), Int((a + b*x)*FresnelS(a + b*x)*sin(Pi*(a + b*x)**S(2)/S(2)), x), x) + Simp((a …
876 …(2)*b/(m + S(1)), Int(x**(m + S(1))*FresnelS(b*x)*sin(Pi*b**S(2)*x**S(2)/S(2)), x), x) + Simp(x**(…
892 …))/(Pi*b**S(2)), Int(x**(m + S(-2))*FresnelS(b*x)*cos(Pi*b**S(2)*x**S(2)/S(2)), x), x) - Simp(x**(…
[all …]

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