Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.adrh)

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=11/4, b_1`>=-11/2

For fixed z and a₁=11/4, b_1`=-7/2

http://functions.wolfram.com/07.22.03.adrh.01

Input Form

HypergeometricPFQ[{11/4}, {-(7/2), -(19/4)}, -z] == (1/(145166175 z^(1/4))) (Sqrt[2] (-7 (-20738025 - 38045700 z - 7650720 z^2 + 7761600 z^3 - 2350080 z^4 - 1818624 z^5 + 1835008 z^6) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-145166175 - 72765000 z + 80332560 z^2 - 25361280 z^3 + 3655680 z^4 - 14450688 z^5 + 524288 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (145166175 - 120789900 z + 43853040 z^2 - 11370240 z^3 + 5591040 z^4 + 2818048 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)

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]