Contiguous relations of hypergeometric series

Abstract

The 15 Gauss contiguous relations for ${}_2{F}_1$ hypergeometric series imply that any three ${}_2{F}_1$ series whose corresponding parameters differ by integers are linearly related (over the field of rational functions in the parameters). We prove several properties of coefficients of these general contiguous relations, and use the results to propose effective ways to compute contiguous relations. We also discuss contiguous relations of generalized and basic hypergeometric functions, and several applications of them.

12 pages; full bibliography added. This is the published text, with corrected formulas (24)-(25)

Cited by in corpus (20)

• HypExp 2, Expanding Hypergeometric Functions about Half-Integer Parameters
• Gauss hypergeometric function: reduction, epsilon-expansion for integer/half-integer parameters and Feynman diagrams
• Towards all-order Laurent expansion of generalized hypergeometric functions around rational values of parameters
• Fast computation of the Gauss hypergeometric function with all its parameters complex with application to the Poschl-Teller-Ginocchio potential wave functions
• All order epsilon-expansion of Gauss hypergeometric functions with integer and half/integer values of parameters
• On the all-order epsilon-expansion of generalized hypergeometric functions with integer values of parameters
• Real zeros of 2F1 hypergeometric polynomials
• A Hypergeometric Integral with Applications to the Fundamental Solution of Laplace's Equation on Hyperspheres
• Transformations of algebraic Gauss hypergeometric functions
• On Some Hypergeometric Summations
• Bernstein-Type Bounds for Beta Distribution
• Three term relations for basic hypergeometric series
• Belyi maps from zeroes of hypergeometric polynomials
• Periods of Hodge cycles and special values of the Gauss' hypergeometric function
• Transformation formulas and three-term relations for basic hypergeometric series
• Contiguous relations of ${}_3{\varphi }_2$-series
• Duality and Reciprocity for Hypergeometric Series with Gamma Product Formula
• The symmetries of the 2phi1
• Linear relations for Lauricella $F_D$ functions and symmetric polynomial
• P-finite Recurrences From Generating Functions with Roots of Polynomials