1
2COMMENT simple tests of hypergeometric operator;
3
4hypergeometric ({},{},z);
5
6hypergeometric ({1/2,1},{3/2},-x^2);
7
8hypergeometric ({1,1},{2},z);
9
10hypergeometric ({1/2,1/2},{3/2},z^2);
11
12hypergeometric ({1/2,1/2},{3/2},-z^2);
13
14hypergeometric ({a,b},{b},z);
15
16hypergeometric ({a,a+1/2},{1/2},z^2);
17
18hypergeometric ({a,a+1/2},{1/2},-tan(z)^2);
19
20hypergeometric ({a,a+1/2},{3/2},z^2);
21
22hypergeometric ({a,a+1/2},{3/2},-tan(z)^2);
23
24
25hypergeometric ({-a,a},{1/2},-z^2);
26
27hypergeometric ({-a,a},{1/2},sin(z)^2);
28
29hypergeometric ({-a,a},{3/2},-z^2);
30
31hypergeometric ({-a,a},{3/2},sin(z)^2);
32
33hypergeometric ({a,1-a},{3/2},-z^2);
34
35hypergeometric ({a,1-a},{3/2},sin(z)^2);
36
37hypergeometric ({a,a+1/2},{2*a+1},z);
38
39hypergeometric ({a,a+1/2},{2*a},z);
40
41hypergeometric ({a+1,b},{a},z);
42
43hypergeometric ({a,b},{c},1);
44
45hypergeometric ({a,b},{a-b+1},-1);
46
47hypergeometric ({1,a},{a+1},-1);
48
49hypergeometric ({a,b},{(a+b+1)/2},1/2);
50
51hypergeometric ({a,b},{(a+b)/2+1},1/2);
52
53hypergeometric ({a,1-a},{b},1/2);
54
55df(hypergeometric({a,b},{c},z),z);
56
57hypergeometric ({a,b,c},{a-b+1,a+c-1},1);
58
59hypergeometric ({a,b,c},{a-b+1,a+c-1},z);
60
61hypergeometric ({a,b,c},{(a+b+1)/2,2*c},1);
62
63hypergeometric ({a,1-a,c},{d,2*c-d+1},1);
64
65hypergeometric ({a,b},{a-b+1},-1);
66
67hypergeometric ({1,b},{b+1},-1);
68
69hypergeometric ({2,b},{b+1},-1);
70
71hypergeometric ({a,b},{c,b},z);
72
73% Legendre functions
74hypergeometric ({a,b},{2*b},z);
75
76
77
78COMMENT simple tests of MeijerG operator;
79
80MeijerG({{},1},{{0}},x);  % should be 1/2(sign( - abs(x) + 1) - sign(abs(x) + 1))
81
82MeijerG({{},a},{{b}},x);
83
84MeijerG({{1}},{{},0},x);  % should be 1-1/2(sign( - abs(x) + 1) - sign(abs(x) + 1))
85
86MeijerG({{a}},{{},b},x);
87
88MeijerG({{}},{{0}},-x);   % exp(x)
89
90MeijerG({{}},{{b}},x);
91
92MeijerG({{a}},{{b}},z);
93
94%MeijerG({{a}},{{b},a-1},z);
95
96%MeijerG({{a}},{{b},2*a-b-1},z);
97
98MeijerG({{a}},{{a-1/2},a-1},z);
99
100MeijerG({{a}},{{a},a-1},z);
101
102MeijerG({{a}},{{a},a-1/2},z);
103
104MeijerG({{a},a+1/2},{{a-1/2}},z);
105
106MeijerG({{a},a+1/2},{{a}},z);
107
108MeijerG({{a},a+1},{{a}},z);
109
110MeijerG({{a},a+1/2},{{a},a-1/2},z);
111
112MeijerG({{a},a},{{a-1/2},a-1/2},z);
113
114MeijerG({{a,a+1/2}},{{a}},z);
115
116MeijerG({{a,a}},{{a}},z);
117
118MeijerG({{a}},{{a,a}},z);
119
120
121% to force simplification of some sqrt expressions
122off precise;
123
124MeijerG({{}},{{0},1/2},x^2/4) * sqrt(pi); % cosine
125
126MeijerG({{}},{{1/2},0},x^2/4) * sqrt(pi);  % sine
127
128% hyperbolic cosine and sine
129MeijerG({{}},{{0},1/2},-x^2/4) * sqrt(pi);
130
131
132MeijerG({{}},{{1/2},0},-x^2/4) * sqrt(pi);
133
134
135% inverse sine
136-i/(2*sqrt(pi)) * MeijerG({{1,1}},{{1/2},0},-x^2);
137
138% inverse tangent
1391/2 * MeijerG({{1/2,1}},{{1/2},0},x^2);
140
141% inverse cotangent
1421/2 * MeijerG({{1/2},1},{{1/2,0}},x^2);
143
144% inverse hyperbolic sine
145MeijerG({{1,1}},{{1/2},0},x^2);
146
147MeijerG({{a,a}},{{a-1/2},a-1},x^2);
148
149MeijerG({{1,1}},{{1},0},x);
150
151MeijerG({{}},{{1+1/4},1-1/4},(x^2)/4) * sqrt pi;
152
153MeijerG({{}},{{b,b+1/2}},z);
154
155%% wrong ??
156%%MeijerG({{},a,a},{{a-1,a-1}},z);
157
158%MeijerG({{}},{{b,b+1/3,b+2/3}},z);
159
160end;
161
162