Generating Kummer Type Formulas for Hypergeometric Functions
Generating Kummer Type Formulas for Hypergeometric Functions Nobuki Takayama Kobe University, Rokko, Kobe 657-8501, Japan, [email protected]
Abstract. Kummer type formulas are identities of hypergeometric series. A symmetry by the permutations of n-letters yields these formulas. We will present an algorithmic method to derive known and new Kummer type formulas. The algorithm utilizes several algorithms in algebra and geometry for generating Kummer type formulas.
1
Introduction
The Gauss hypergeometric function is defined by the series F (a, b, c; x) =
∞ X (a)n (b)n n x , (1)n (c)n n=0
(a)n = a(a+1) · · · (a+n−1) = Γ (a+n)/Γ (a)
where a, b, c are complex parameters and we assume c 6∈ Z
Abstract. Kummer type formulas are identities of hypergeometric series. A symmetry by the permutations of n-letters yields these formulas. We will present an algorithmic method to derive known and new Kummer type formulas. The algorithm utilizes several algorithms in algebra and geometry for generating Kummer type formulas.
1
Introduction
The Gauss hypergeometric function is defined by the series F (a, b, c; x) =
∞ X (a)n (b)n n x , (1)n (c)n n=0
(a)n = a(a+1) · · · (a+n−1) = Γ (a+n)/Γ (a)
where a, b, c are complex parameters and we assume c 6∈ Z
