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On the Analytic Continuation of Lauricella–Saran Hypergeometric Function F K ( a 1 , a 2 , b 1 , b 2 ; a 1 , b 2 , c 3 ; z )

Author

Listed:
  • Tamara Antonova

    (Institute of Applied Mathematics and Fundamental Sciences, Lviv Polytechnic National University, 12 Stepan Bandera Str., 79000 Lviv, Ukraine)

  • Roman Dmytryshyn

    (Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine)

  • Vitaliy Goran

    (Faculty of Mathematics and Computer Science, Vasyl Stefanyk Precarpathian National University, 57 Shevchenko Str., 76018 Ivano-Frankivsk, Ukraine)

Abstract

The paper establishes an analytical extension of two ratios of Lauricella–Saran hypergeometric functions F K with some parameter values to the corresponding branched continued fractions in their domain of convergence. The PC method used here is based on the correspondence between a formal triple power series and a branched continued fraction. As additional results, analytical extensions of the Lauricella–Saran hypergeometric functions F K ( a 1 , a 2 , 1 , b 2 ; a 1 , b 2 , c 3 ; z ) and F K ( a 1 , 1 , b 1 , b 2 ; a 1 , b 2 , c 3 ; z ) to the corresponding branched continued fractions were obtained. To illustrate this, we provide some numerical experiments at the end.

Suggested Citation

  • Tamara Antonova & Roman Dmytryshyn & Vitaliy Goran, 2023. "On the Analytic Continuation of Lauricella–Saran Hypergeometric Function F K ( a 1 , a 2 , b 1 , b 2 ; a 1 , b 2 , c 3 ; z )," Mathematics, MDPI, vol. 11(21), pages 1-18, October.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:21:p:4487-:d:1270678
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    References listed on IDEAS

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    1. T. Hutchinson, 1981. "Compound gamma bivariate distributions," Metrika: International Journal for Theoretical and Applied Statistics, Springer, vol. 28(1), pages 263-271, December.
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