충청수학회지 (Journal of the Chungcheong Mathematical Society)

  • 제24권2호
  • /
  • Pages.187-204
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  • 2011
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  • 1226-3524(pISSN)
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  • 2383-6245(eISSN)
충청수학회 (The Chungcheong Mathematical Society)
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FUNCTIONAL RELATIONS INVOLVING SRIVASTAVA'S HYPERGEOMETRIC FUNCTIONS HB AND F(3)

  • 투고 : 2011.01.13
  • 심사 : 2011.05.13
  • 발행 : 2011.06.30
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초록

B. C. Carlson [Some extensions of Lardner's relations between $_0F_3$ and Bessel functions, SIAM J. Math. Anal. 1(2) (1970), 232-242] presented several useful relations between Bessel and generalized hypergeometric functions that generalize some earlier results. Here, by simply splitting Srivastava's hypergeometric function $H_B$ into eight parts, we show how some useful and generalized relations between Srivastava's hypergeometric functions $H_B$ and $F^{(3)}$ can be obtained. These main results are shown to be specialized to yield certain relations between functions $_0F_1$, $_1F_1$, $_0F_3$, ${\Psi}_2$, and their products including different combinations with different values of parameters and signs of variables. We also consider some other interesting relations between the Humbert ${\Psi}_2$ function and $Kamp\acute{e}$ de $F\acute{e}riet$ function, and between the product of exponential and Bessel functions with $Kamp\acute{e}$ de $F\acute{e}riet$ functions.

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