Explicit representations of dihedral Gauss hypergeometric functions
Ramanujan Journal, cilt.70, sa.4, 2026 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 70 Sayı: 4
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s11139-026-01403-8
- Dergi Adı: Ramanujan Journal
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Dihedral Gauss hypergeometric functions, Jacobi polynomials, Trigonometric Pöschl–Teller potential
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Orta Doğu Teknik Üniversitesi Adresli: Evet
Özet
Solutions of the Gauss hypergeometric equation, two of whose characteristic exponent differences are half-odd-integers and the third is an arbitrary complex number, are called dihedral Gauss hypergeometric functions. They can be expressed in terms of elementary functions since they belong to Schwarz’s dihedral class. In this article, explicit trigonometric and algebraic identities for dihedral Gauss hypergeometric functions in terms of the Jacobi polynomials with some pre-factors are presented. To this end, four different sets of linearly independent solutions of a specific ordinary differential equation are obtained where the first three sets contain dihedral Gauss hypergeometric functions and the fourth one consists of elementary functions. Dihedral identities are then obtained by expressing the hypergeometric solutions as linear combinations of the elementary ones. Moreover, dihedral identities are extended to a more general class of Gauss hypergeometric functions.