The Clausenian hypergeometric function ${}_3{F}_2$ with unit argument and negative integral parameter differences

Abstract

New explicit as well as manifestly symmetric three-term summationformulas are derived for the Clausenian hypergeometric series ${}_3{F}_2(1)$ with negative integral parameter differences. Our results generalize and naturally extend several similar relations published, in recent years, by many authors. An appropriate and useful connection is established with the quite underestimated 1974 paper by P. W. Karlsson.

Journal version

References in corpus (12)

• Horava-Lifshitz gravity: a status report
• Critical behavior at m-axial Lifshitz points: field-theory analysis and $\epsilon$-expansion results
• Two-loop renormalization-group analysis of critical behavior at m-axial Lifshitz points
• A massive Feynman integral and some reduction relations for Appell functions
• Large-n expansion for m-axial Lifshitz points
• Lifshitz-point correlation length exponents from the large-n expansion
• On conjectured local generalizations of anisotropic scale invariance and their implications
• On two Thomae-type transformations for hypergeometric series with integral parameter differences
• On Some Sums of Digamma and Polygamma functions - Version (2017) and Review
• 447 Instances of Hypergeometric 3F2(1)
• A note on some summations due to Ramanujan, their generalization and some allied series
• On Hypergeometrics 3F2(1) - A Review

Cited by in corpus (3)

• Hypergeometric Functions at Unit Argument: Simple Derivation of Old and New Identities
• Feynman integral in ${\mathbb{R}}^1\oplus {\mathbb{R}}^m$ and complex expansion of ${}_2{F}_1$
• On the Very-well-poised Bilateral Basic Hypergeometric ${}_5{\psi }_5$ Series