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

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`=-9/2

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

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), -(11/4)}, -z] == (1/(14371451325 z^(1/4))) (Sqrt[2] ((-(-14371451325 - 22065258600 z + 94802400 z^2 + 6724650240 z^3 + 34516500480 z^4 + 131263414272 z^5 - 33472118784 z^6 + 331350016 z^7)) BesselJ[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (-14371451325 - 2903323500 z + 7615792800 z^2 - 1807565760 z^3 + 19748136960 z^4 + 42452877312 z^5 - 2319974400 z^6 + 4194304 z^7) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + 4 z (14371451325 - 16258611600 z + 10412463600 z^2 - 8831370240 z^3 + 5806632960 z^4 - 6687424512 z^5 + 79691776 z^6) 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]