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

Abstract

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.

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Acknowledgements

The authors thank the referee for valuable suggestions that led to a better presentation of the paper. The financial assistance provided to the second author in the form of a Senior Research Fellowship from Council of Scientific and Industrial Research, India is gratefully acknowledged.

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Correspondence to Vivek Sahai.

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Çekim, B., Dwivedi, R., Sahai, V. et al. Certain Integral Representations, Transformation Formulas and Summation Formulas Related to Humbert Matrix Functions. Bull Braz Math Soc, New Series (2020). https://doi.org/10.1007/s00574-020-00198-6

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Keywords

  • Special matrix functions
  • Matrix functional calculus

Mathematics Subject Classification

  • 15A15
  • 33C65