Journal of the Chungcheong Mathematical Society (충청수학회지)

The Chungcheong Mathematical Society (충청수학회)
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DECOMPOSITION FORMULAS AND INTEGRAL REPRESENTATIONS FOR THE KAMPÉ DE FÉRIET FUNCTION F0:3;32:0;0 [x, y]

  • Received : 2010.06.23
  • Accepted : 2010.11.09
  • Published : 2010.12.30
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Abstract

By developing and using certain operators like those initiated by Burchnall-Chaundy, the authors aim at investigating several decomposition formulas associated with the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y]. For this purpose, many operator identities involving inverse pairs of symbolic operators are constructed. By employing their decomposition formulas, they also present a new group of integral representations of Eulerian type for the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ function $F_{2:0;0}^{0:3;3}$ [x, y], some of which include several hypergeometric functions such as $_2F_1$, $_3F_2$, an Appell function $F_3$, and the $Kamp{\acute{e}}$ de $F{\acute{e}}riet$ functions $F_{2:0;0}^{0:3;3}$ and $F_{1:0;1}^{0:2;3}$.

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References

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