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<p>A generalization of the extended gamma matrix function (EGMF) and extended beta matrix function (EBMF) is introduced using the four-parameter Mittag-Leffler matrix function. Several fundamental properties are explored. Furthermore, we establish extended hypergeometric matrix function (EHGMF) and extended confluent hypergeometric matrix function (ECHGMF) by utilizing the newly generalized extended beta function. Various properties of these functions are examined, such as their integral representations, differentiation formulas, transformation formulas, beta transforms, recurrence relations and generating functions.</p>

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Extended matrix variate hypergeometric function and its related functions

  • 期刊论文

  • 发表日期：

    2025年10月15日

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  • K. M. Bhammar,
  • R. K. Jana

摘要

A generalization of the extended gamma matrix function (EGMF) and extended beta matrix function (EBMF) is introduced using the four-parameter Mittag-Leffler matrix function. Several fundamental properties are explored. Furthermore, we establish extended hypergeometric matrix function (EHGMF) and extended confluent hypergeometric matrix function (ECHGMF) by utilizing the newly generalized extended beta function. Various properties of these functions are examined, such as their integral representations, differentiation formulas, transformation formulas, beta transforms, recurrence relations and generating functions.