A Study of Appell Function of Two Variables Using Hurwitz - Lerch Zeta Function of Two Variables


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Authors

  • Archna Jaiswal Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya, Uttar Pradesh, India
  • S. K. Raizada Department of Mathematics and Statistics, Dr. Rammanohar Lohia Avadh University, Ayodhya, Uttar Pradesh, India

Keywords:

Generalized Hurwitz-Lerch Zeta Function, Gamma Function, Beta Function, Hypergeometric Function, Binomial Series, Eulerian integral

Abstract

Firstly, the Appell's Hypergeometric Function of two variables $F_{2}[a, b_{1}, b_{2};c_{1},c_{2};x_{1},x_{2}]$ is introduced using Hurwitz-Lerch Zeta Function of two variables $\phi_{a_1,a_2,b_1,b_2;c_1c_2} (x_1, x_2, s, p)$. Then several integral representations and differential formula are investigated for this function $F_{2}[a, b_{1},b_{2};c_{1},c_{2};x_{1},x_{2}]$. The function $F_{2}[a,b_{1},b_{2};c_{1},c_{2};x_{1},x_{2}]$ that we have introduced \& defined here has also been represented in term of generalized Hypergeometric Function ${}_{p}F_{q}$. To strengthen our main results, we have also considered some important special cases.

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Published

15-06-2024

How to Cite

Archna Jaiswal, & S. K. Raizada. (2024). A Study of Appell Function of Two Variables Using Hurwitz - Lerch Zeta Function of Two Variables. International Journal of Mathematics And Its Applications, 12(2), 95–103. Retrieved from https://ijmaa.in/index.php/ijmaa/article/view/1451

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Section

Research Article