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

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.accu.01

Input Form

HypergeometricPFQ[{5/4}, {-(11/2), -(17/4)}, z] == -((1/(103378275 Sqrt[2])) (z^(1/4) ((-103378275 - 212284800 z - 135535680 z^2 - 28984320 z^3 - 3608064 z^4 - 442368 z^5 + 131072 z^6) BesselI[-(1/4), Sqrt[z]]^2 + 4 Sqrt[z] (103378275 + 129582180 z + 39221280 z^2 + 5917248 z^3 + 645120 z^4 + 81920 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 4 z (-103378275 - 46879560 z - 9068976 z^2 - 1090944 z^3 - 122880 z^4 + 32768 z^5) BesselI[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]