Completely monotonic ratios of basic and ordinary gamma functions

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Berg C., Cetinkaya A., Karp D.

AEQUATIONES MATHEMATICAE, cilt.95, sa.3, ss.569-588, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 95 Sayı: 3
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00010-020-00767-6
  • Dergi Adı: AEQUATIONES MATHEMATICAE
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Sayfa Sayıları: ss.569-588
  • İstanbul Kültür Üniversitesi Adresli: Evet

Özet

We investigate conditions for logarithmic complete monotonicity of product ratios of gamma and q-gamma functions whose arguments are linear functions of the variable. We give necessary and sufficient conditions in terms of nonnegativity of a certain explicitly written measure in the q case and of a certain elementary function in the classical q=1 case. In the latter case we further provide simple new sufficient conditions leading to many new examples of logarithmically completely monotonic gamma ratios. Finally, we apply some of our results to study monotonicity of some gamma ratios and rational functions.