Some summation theorems for Clausen's hypergeometric functions with unit argument

2018/06/06 by Qureshi, M. I., Shadab, Mohd
#11J81 #33B15 #33C05 #33C20 #33C90 #Classical Analysis and ODEs (math.CA) #FOS: Mathematics

paper · doi:10.48550/arxiv.1806.07949

Abstract

Motivated by the work on hypergeometric summation theorems (recorded in the table III of Prudnikov et al. pp. 541-546), we have established some new summation theorems for Clausen's hypergeometric functions with unit argument in terms of π and natural logarithms of some rational and irrational numbers. Also, we have given some modified summation theorems for Clausen's hypergeometric functions.

Related

• Some summation theorems for truncated Clausen series and applications
• Some decomposition formulas of generalized hypergeometric functions and formulas of an analytic continuation of the Clausen function
• Polynomial perturbations of Euler's and Clausen's identities
• πand other formulae implied by hypergeometric summation theorems
• π-formulas with free parameters