hypergeo0 http://www.math.kobe-u.ac.jp/OCD/ 2003-04-01 2002-11-29 0 0 experimental alg1 arith1 calculus1 complex1 fns1 integer1 interval1 logic1 nums1 relation1 This CD defines some basic hypergeometric integrals and symbols necessary to define hypergeometric functions. These functions are described in the following books. (1) Handbook of Mathematical Functions, Abramowitz, Stegun (2) Higher transcendental functions. Vol. III. Krieger Publishing Co., Inc., Melbourne, Fla., 1981, Erdlyi, Arthur; Magnus, Wilhelm; Oberhettinger, Fritz; Tricomi, Francesco G. (3) From Gauss to Painleve, Vieweg, Katsunori Iwasaki, Hironobu Kimura, Shun Shimomura, Masaaki Yoshida gamma Euler's gamma function gamma(z)=\int_0^{+\infty} t^{z-1} e^{-z} dt (Re(z)>0) 0 0 1 gamma(n) = (n-1)! (n \in N) 1 beta Euler's beta function beta(p,q)=\frac{gamma(p)gamma(q)}{gamma(p+q)}(p,q \not\in Z_{<=0}) beta(p,q)=\int_0^1 t^{p-1} (1-t)^{q-1} dt (Re(p),Re(q)>0) 0 0 0 1 1 1 1 pochhammer Pochhammer symbol pochhammer(a,n) = gamma(a+n)/gamma(a) pochhammer(a,n) = \prod_0^{n-1} (a+i) 0 1