Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agq0)

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.agq0.01

Input Form

HypergeometricPFQ[{23/4}, {9/2, -(23/4)}, z] == (1/(7595252280 Sqrt[2] z^(9/4))) ((-4 z (554624445375 + 173415710160 z + 39104755200 z^2 + 1762467840 z^3 - 731185152 z^4 + 1048576 z^5) BesselI[1/4, Sqrt[z]]^2 + 4 Sqrt[z] (2773122226875 + 1132566435000 z + 238852575360 z^2 + 28329799680 z^3 - 3778805760 z^4 - 287834112 z^5 + 8388608 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - (13865611134375 + 6895330942500 z + 1579536504000 z^2 + 232799938560 z^3 - 7194378240 z^4 - 3763077120 z^5 + 29360128 z^6) BesselI[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]