% Test cases for hypergeometric functions
% from Wolfram Koepf: Power Series in Computer Algebra
% J. Symbolic Computation 13, (1992)
load_package specfn2;
hypergeometric({-alpha},{},x);
hypergeometric({},{},x);
x * hypergeometric({1,1},{2},x);
x * hypergeometric({},{3/2},-x^2/4);
hypergeometric({},{1/2},-x^2/4);
x * hypergeometric({},{3/2},x^2/4);
hypergeometric({},{1/2},x^2/4);
x * hypergeometric({1/2,1/2},{3/2},x^2);
x * hypergeometric({1/2,1},{3/2},-x^2);
x * hypergeometric({1/2,1/2},{3/2},-x^2);
x * hypergeometric({1/2,1},{3/2},x^2);
% another example which shows the polynomial case:
hypergeometric({12,12/34},{3},x);
% 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);
% is known for integers though
hypergeometric({a,b,-4},{c,a+b-c-4+1},z);
hypergeometric({1-c-2n,-2n},{c},1);
hypergeometric({a,b},{1+b-a},-1); % Kummer's formula (z=1)
hypergeometric({a,b},{c},1);
end;