Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8570)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8570.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), -(23/4)}, z] == (1/(1430923725 z^(1/4))) (Sqrt[2] ((1430923725 - 3152179800 z + 1571724000 z^2 + 182198016 z^3 + 3677184 z^4 - 688128 z^5 + 262144 z^6) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-476974575 + 414760500 z + 150242400 z^2 + 4888128 z^3 - 57344 z^4 + 32768 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (1430923725 + 663616800 z + 70686000 z^2 - 854784 z^3 + 122880 z^4 - 65536 z^5) 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]