Hypergeometric series and divided differences

Creative Commons License

Zürnacı Yetiş F., Dişibüyük N. B.

Constructive Functions 2025 in conjunction with the 37th Shanks Lecture Celebrating Ed Saff's 80th birthday, Tennessee, United States Of America, 19 - 22 May 2025, pp.68, (Summary Text)

  • Publication Type: Conference Paper / Summary Text
  • City: Tennessee
  • Country: United States Of America
  • Page Numbers: pp.68
  • Dokuz Eylül University Affiliated: Yes

Abstract

Divided differences and hypergeometric series are intimately related. In this work, divided differences
provide new proofs for some well-known hypergeometric series identities in addition to the existing
proofs in the literature. The proofs of Chu-Vandermonde, Pfaff-Saalsch¨utz, and one of Thomae’s 3F2
transformation formulas are established by a method based on divided differences. The proofs of
the q-versions of these formulas, q-Chu-Vandermonde, q-Pfaff-Saalsch¨utz, and Sear’s Transformation
formulas, are also derived by using divided differences.