Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab05)

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=-3/4, b_1`>=-11/2

For fixed z and a₁=-3/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.ab05.01

Input Form

HypergeometricPFQ[{-(3/4)}, {11/2, 3/4}, -z] == (1/(56576 Sqrt[2] z^(15/4))) ((4 z (121275 + 13860 z + 5184 z^2 + 17408 z^3 + 8192 z^4) BesselJ[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (363825 - 27720 z + 4032 z^2 + 6144 z^3 + 4096 z^4) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (1091475 - 291060 z + 17136 z^2 + 16128 z^3 + 61440 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]