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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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