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

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=-5/4, b_1`>=-11/2

For fixed z and a₁=-5/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{-(5/4)}, {11/2, 21/4}, -z] == (221 (2 Sqrt[z] (-885809925 + 858931920 z - 303367680 z^2 + 137601024 z^3 + 42139648 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]]^2 - 3 (-1476349875 + 1126818000 z - 368417280 z^2 + 102277120 z^3 + 41222144 z^4 + 1048576 z^5) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 2 Sqrt[z] (-1634873625 + 1120165200 z - 368248320 z^2 + 107028480 z^3 + 41353216 z^4 + 1048576 z^5) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(12128714752 Sqrt[2] z^(15/4))

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]