Honam Mathematical Journal (호남수학학술지)

The Honam Mathematical Society (호남수학회)
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CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5

  • Received : 2010.07.12
  • Accepted : 2010.08.10
  • Published : 2010.09.25
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Abstract

Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

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References

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Cited by

  1. Relations between Lauricella’s triple hypergeometric function FA(3)(x,y,z) and Exton’s function X8 vol.2013, pp.1, 2013, https://doi.org/10.1186/1687-1847-2013-34
  2. Generalization of a Transformation Formula for the Exton's Triple Hypergeometric Series X12and X17 vol.54, pp.4, 2014, https://doi.org/10.5666/KMJ.2014.54.4.677