hypergeo1 http://www.math.kobe-u.ac.jp/OCD/ 2003-07-26 2002-11-29 0 0 experimental alg1 arith1 calculus1 fns1 hypergeo0 interval1 linalg1 linalg4 nums1 relation1 This CD defines the Gauss hypergeometric function, confluent hypergeometric functions, and generalized hypergeometric functions in one variable. 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. hypergeometric0F1 Hypergeometric function {}_0 F_1. hypergeometric0F1(;a;z) =\sum_{n=0}^{+\infty} \frac{1}{pochhammer(a,n)pochhammer(1,n)} z^n 0 1 1 hypergeometric1F1 Kummer's confluent hypergeometric function. hypergeometric1F1(a,b;z) =\sum_{n=0}^{+\infty} \frac{pochhammer(a,n)}{pochhammer(1,n)pochhammer(b,n)} z^n 0 1 hypergeometric2F1 The Gauss hypergeometric function. This function has a branch cut on [1,+infinity). hypergeometric2F1(a,b,c;z) =\sum_{n=0}^{+\infty} \frac{pochhammer(a,n)pochhammer(b,n)}{pochhammer(c,n)pochhammer(1,n)} z^n 0 1 z (1-z) d^2 F/dz^2 + (c - (a+b+1) z) d F/dz - a b F = 0 1 1 0 hypergeometric_pFq Generalized hypergeometric function. This function has a branch cut on [1,+infinity). hypergeometric_pFq(a,b;z) =\sum_{n=0}^{+\infty} \frac{\Pi_i pochhammer(a_i,n)}{\Pi_i pochhammer(b_i,n)pochhammer(1,n)} z^n 0 1 1 1