Codemist Standard Lisp 3.54 for DEC Alpha: May 23 1994
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% Test cases for hypergeometric functions
% from Wolfram Koepf: Power Series in Computer Algebra
% J. Symbolic Computation 13, (1992)
load_package specfn2;
*** erfc already defined as operator
(specfn2)
hypergeometric({-alpha},{},x);
*** hypergeometric declared operator
hypergeometric({ - alpha},{},x)
hypergeometric({},{},x);
hypergeometric({},{},x)
x * hypergeometric({1,1},{2},x);
hypergeometric({1,1},{2},x)*x
x * hypergeometric({},{3/2},-x^2/4);
2
3 - x
hypergeometric({},{---},-------)*x
2 4
hypergeometric({},{1/2},-x^2/4);
2
1 - x
hypergeometric({},{---},-------)
2 4
x * hypergeometric({},{3/2},x^2/4);
2
3 x
hypergeometric({},{---},----)*x
2 4
hypergeometric({},{1/2},x^2/4);
2
1 x
hypergeometric({},{---},----)
2 4
x * hypergeometric({1/2,1/2},{3/2},x^2);
1 1 3 2
hypergeometric({---,---},{---},x )*x
2 2 2
x * hypergeometric({1/2,1},{3/2},-x^2);
1 3 2
hypergeometric({---,1},{---}, - x )*x
2 2
x * hypergeometric({1/2,1/2},{3/2},-x^2);
1 1 3 2
hypergeometric({---,---},{---}, - x )*x
2 2 2
x * hypergeometric({1/2,1},{3/2},x^2);
1 3 2
hypergeometric({---,1},{---},x )*x
2 2
% another example which shows the polynomial case:
hypergeometric({12,12/34},{3},x);
6
hypergeometric({12,----},{3},x)
17
% Some more (nontrivial) examples from
% Graham, Knuth, Ptashnik: Concrete Mathematics
% Addison-Wesley Publishing Company, 1989
HYPERGEOMETRIC({a,b,-n},{c,a+b-c-n+1},1);
hypergeometric({a,b, - n},{c,a + b - c - n + 1},1)
% is known for integers though
hypergeometric({a,b,-4},{c,a+b-c-4+1},z);
hypergeometric({a,b,-4},{c,a + b - c - 3},z)
hypergeometric({1-c-2n,-2n},{c},1);
hypergeometric({ - c - 2*n + 1, - 2*n},{c},1)
hypergeometric({a,b},{1+b-a},-1);
hypergeometric({a,b},{ - a + b + 1},-1)
% Kummer's formula (z=1)
hypergeometric({a,b},{c},1);
hypergeometric({a,b},{c},1)
end;
(TIME: ghyper 250 266)
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