Certain Integral Representations, Transformation Formulas and Summation Formulas Related to Humbert Matrix Functions

ÇEKİM B., Dwivedi R., Sahai V., Shehata A.

BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY, cilt.52, sa.2, ss.213-239, 2021 (SCI-Expanded) identifier identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 52 Sayı: 2
  • Basım Tarihi: 2021
  • Doi Numarası: 10.1007/s00574-020-00198-6
  • Dergi Adı: BULLETIN OF THE BRAZILIAN MATHEMATICAL SOCIETY
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, MathSciNet, zbMATH
  • Sayfa Sayıları: ss.213-239
  • Anahtar Kelimeler: Special matrix functions, Matrix functional calculus, APPELL
  • Gazi Üniversitesi Adresli: Evet

Özet

The main objective of this work is to present some important results and formulas in the theory of Humbert matrix functions by using the concepts of matrix functional calculus. We define Humbert matrix functions assuming that not all the matrices involved are commuting. We show that these two variable Humbert matrix functions follow naturally as confluent cases of Appell matrix functions. We determine their regions of convergence, integral representations, transformation formulas, summation formulas, contiguous relations and matrix differential equations satisfied by them.