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

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=5/2

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

Input Form

HypergeometricPFQ[{23/4}, {5/2, -(15/4)}, -z] == (1/(76039425 z^(1/4))) (Sqrt[2] ((76039425 + 218264256 z + 124328448 z^2 + 13369344 z^3 + 4259840 z^4) BesselJ[1/4, Sqrt[z]]^2 - 8 Sqrt[z] (50237145 + 25083648 z - 12203520 z^2 - 3293184 z^3 + 65536 z^4) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (122174325 + 57481920 z - 173846016 z^2 - 30277632 z^3 - 3866624 z^4) 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]