Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ad8z)

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=9/4, b_1`>=-11/2

For fixed z and a₁=9/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.ad8z.01

Input Form

HypergeometricPFQ[{9/4}, {-(11/2), -(13/4)}, -z] == (1/(30405375 Sqrt[2])) (z^(1/4) ((30405375 - 64638000 z + 44755200 z^2 - 12326400 z^3 + 2880000 z^4 + 81920 z^5 + 131072 z^6) BesselJ[-(1/4), Sqrt[z]]^2 + 12 Sqrt[z] (10135125 - 13437900 z + 4888800 z^2 - 1064640 z^3 + 235520 z^4 + 147456 z^5) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] - 4 z (-30405375 + 15989400 z - 4037040 z^2 + 835200 z^3 + 122880 z^4 + 32768 z^5) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^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]