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, Amerika Birleşik Devletleri, 19 - 22 Mayıs 2025, ss.68, (Özet Bildiri)

  • Yayın Türü: Bildiri / Özet Bildiri
  • Basıldığı Şehir: Tennessee
  • Basıldığı Ülke: Amerika Birleşik Devletleri
  • Sayfa Sayıları: ss.68
  • Dokuz Eylül Üniversitesi Adresli: Evet

Özet

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.