Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9853)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-5/2

http://functions.wolfram.com/07.22.03.9853.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(5/2), 11/4}, -z] == -((1/(45298483200 z^(7/4))) (7 (Sqrt[Pi] (890127225 + 1675533600 z - 5155488000 z^2 + 2444083200 z^3 - 651755520 z^4 + 320864256 z^5 + 16777216 z^6) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (296709075 - 386028720 z + 165957120 z^2 - 44064768 z^3 + 19857408 z^4 + 1048576 z^5) Cos[2 Sqrt[z]] + (-890127225 - 726064560 z + 230376960 z^2 - 55664640 z^3 + 19070976 z^4 + 1048576 z^5) Sin[2 Sqrt[z]]))))

Standard Form

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MathML Form

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Rule Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]