1Special
2=======
3
4DiracDelta
5----------
6.. autoclass:: sympy.functions.special.delta_functions.DiracDelta
7   :members:
8
9Heaviside
10---------
11.. autoclass:: sympy.functions.special.delta_functions.Heaviside
12   :members:
13
14Singularity Function
15--------------------
16.. module:: sympy.functions.special.singularity_functions
17
18.. autoclass:: sympy.functions.special.singularity_functions.SingularityFunction
19   :members:
20
21Gamma, Beta and related Functions
22---------------------------------
23.. module:: sympy.functions.special.gamma_functions
24
25.. autoclass:: sympy.functions.special.gamma_functions.gamma
26   :members:
27.. autoclass:: sympy.functions.special.gamma_functions.loggamma
28   :members:
29.. autoclass:: sympy.functions.special.gamma_functions.polygamma
30   :members:
31.. autoclass:: sympy.functions.special.gamma_functions.digamma
32   :members:
33.. autoclass:: sympy.functions.special.gamma_functions.trigamma
34   :members:
35.. autoclass:: sympy.functions.special.gamma_functions.uppergamma
36   :members:
37.. autoclass:: sympy.functions.special.gamma_functions.lowergamma
38   :members:
39.. autoclass:: sympy.functions.special.gamma_functions.multigamma
40   :members:
41.. module:: sympy.functions.special.beta_functions
42.. autoclass:: sympy.functions.special.beta_functions.beta
43   :members:
44
45Error Functions and Fresnel Integrals
46-------------------------------------
47.. module:: sympy.functions.special.error_functions
48
49.. autoclass:: sympy.functions.special.error_functions.erf
50   :members:
51.. autoclass:: sympy.functions.special.error_functions.erfc
52   :members:
53.. autoclass:: sympy.functions.special.error_functions.erfi
54   :members:
55.. autoclass:: sympy.functions.special.error_functions.erf2
56   :members:
57.. autoclass:: sympy.functions.special.error_functions.erfinv
58   :members:
59.. autoclass:: sympy.functions.special.error_functions.erfcinv
60   :members:
61.. autoclass:: sympy.functions.special.error_functions.erf2inv
62   :members:
63
64.. autoclass:: sympy.functions.special.error_functions.FresnelIntegral
65   :members:
66
67.. autoclass:: fresnels
68   :members:
69.. autoclass:: fresnelc
70   :members:
71
72Exponential, Logarithmic and Trigonometric Integrals
73----------------------------------------------------
74
75.. autoclass:: Ei
76   :members:
77.. autoclass:: expint
78   :members:
79.. autofunction:: E1
80.. autoclass:: li
81   :members:
82.. autoclass:: Li
83   :members:
84.. autoclass:: Si
85   :members:
86.. autoclass:: Ci
87   :members:
88.. autoclass:: Shi
89   :members:
90.. autoclass:: Chi
91   :members:
92
93Bessel Type Functions
94---------------------
95
96.. module:: sympy.functions.special.bessel
97
98.. autoclass:: sympy.functions.special.bessel.BesselBase
99   :members:
100
101.. autoclass:: sympy.functions.special.bessel.besselj
102   :members:
103.. autoclass:: sympy.functions.special.bessel.bessely
104   :members:
105.. _besseli:
106.. autoclass:: sympy.functions.special.bessel.besseli
107   :members:
108.. autoclass:: sympy.functions.special.bessel.besselk
109   :members:
110.. autoclass:: sympy.functions.special.bessel.hankel1
111   :members:
112.. autoclass:: sympy.functions.special.bessel.hankel2
113   :members:
114.. autoclass:: sympy.functions.special.bessel.jn
115   :members:
116.. autoclass:: sympy.functions.special.bessel.yn
117   :members:
118
119.. autofunction:: sympy.functions.special.bessel.jn_zeros
120
121.. autoclass:: sympy.functions.special.bessel.marcumq
122   :members:
123
124Airy Functions
125--------------
126
127.. autoclass:: sympy.functions.special.bessel.AiryBase
128   :members:
129
130.. autoclass:: sympy.functions.special.bessel.airyai
131   :members:
132.. autoclass:: sympy.functions.special.bessel.airybi
133   :members:
134.. autoclass:: sympy.functions.special.bessel.airyaiprime
135   :members:
136.. autoclass:: sympy.functions.special.bessel.airybiprime
137   :members:
138
139B-Splines
140---------
141
142.. autofunction:: sympy.functions.special.bsplines.bspline_basis
143.. autofunction:: sympy.functions.special.bsplines.bspline_basis_set
144.. autofunction:: sympy.functions.special.bsplines.interpolating_spline
145
146Riemann Zeta and Related Functions
147----------------------------------
148.. module:: sympy.functions.special.zeta_functions
149
150.. autoclass:: zeta
151   :members:
152.. autoclass:: dirichlet_eta
153   :members:
154.. autoclass:: polylog
155   :members:
156.. autoclass:: lerchphi
157   :members:
158.. autoclass:: stieltjes
159   :members:
160
161Hypergeometric Functions
162------------------------
163.. autoclass:: sympy.functions.special.hyper.hyper
164   :members:
165
166.. autoclass:: sympy.functions.special.hyper.meijerg
167   :members:
168
169.. autoclass:: sympy.functions.special.hyper.appellf1
170   :members:
171
172Elliptic integrals
173------------------
174.. module:: sympy.functions.special.elliptic_integrals
175
176.. autoclass:: elliptic_k
177   :members:
178.. autoclass:: elliptic_f
179   :members:
180.. autoclass:: elliptic_e
181   :members:
182.. autoclass:: elliptic_pi
183   :members:
184
185Mathieu Functions
186-----------------
187.. module:: sympy.functions.special.mathieu_functions
188
189.. autoclass:: sympy.functions.special.mathieu_functions.MathieuBase
190   :members:
191
192.. autoclass:: sympy.functions.special.mathieu_functions.mathieus
193   :members:
194.. autoclass:: sympy.functions.special.mathieu_functions.mathieuc
195   :members:
196.. autoclass:: sympy.functions.special.mathieu_functions.mathieusprime
197   :members:
198.. autoclass:: sympy.functions.special.mathieu_functions.mathieucprime
199   :members:
200
201Orthogonal Polynomials
202----------------------
203
204.. automodule:: sympy.functions.special.polynomials
205
206Jacobi Polynomials
207++++++++++++++++++
208
209.. autoclass:: sympy.functions.special.polynomials.jacobi
210   :members:
211
212.. autofunction:: sympy.functions.special.polynomials.jacobi_normalized
213
214Gegenbauer Polynomials
215++++++++++++++++++++++
216
217.. autoclass:: sympy.functions.special.polynomials.gegenbauer
218   :members:
219
220Chebyshev Polynomials
221+++++++++++++++++++++
222
223.. autoclass:: sympy.functions.special.polynomials.chebyshevt
224   :members:
225
226.. autoclass:: sympy.functions.special.polynomials.chebyshevu
227   :members:
228
229.. autoclass:: sympy.functions.special.polynomials.chebyshevt_root
230   :members:
231
232.. autoclass:: sympy.functions.special.polynomials.chebyshevu_root
233   :members:
234
235Legendre Polynomials
236++++++++++++++++++++
237
238.. autoclass:: sympy.functions.special.polynomials.legendre
239   :members:
240
241.. autoclass:: sympy.functions.special.polynomials.assoc_legendre
242   :members:
243
244Hermite Polynomials
245+++++++++++++++++++
246
247.. autoclass:: sympy.functions.special.polynomials.hermite
248   :members:
249
250Laguerre Polynomials
251++++++++++++++++++++
252
253.. autoclass:: sympy.functions.special.polynomials.laguerre
254   :members:
255.. autoclass:: sympy.functions.special.polynomials.assoc_laguerre
256   :members:
257
258Spherical Harmonics
259-------------------
260
261.. autoclass:: sympy.functions.special.spherical_harmonics.Ynm
262   :members:
263
264.. autofunction:: sympy.functions.special.spherical_harmonics.Ynm_c
265
266.. autoclass:: sympy.functions.special.spherical_harmonics.Znm
267   :members:
268
269Tensor Functions
270----------------
271
272.. autofunction:: sympy.functions.special.tensor_functions.Eijk
273
274.. autofunction:: sympy.functions.special.tensor_functions.eval_levicivita
275
276.. autoclass:: sympy.functions.special.tensor_functions.LeviCivita
277   :members:
278
279.. autoclass:: sympy.functions.special.tensor_functions.KroneckerDelta
280   :members:
281