Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.ab36)

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=-1/4, b_1`>=-11/2

For fixed z and a₁=-1/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.ab36.01

Input Form

HypergeometricPFQ[{-(1/4)}, {-(9/2), 17/4}, z] == -((1/(77070336 Sqrt[2] z^(11/4))) (13 (2 Sqrt[z] (760433751 - 828572976 z - 55625472 z^2 + 2256896 z^3) BesselI[1/4, Sqrt[z]]^2 + 3 (-1267389585 + 2282209776 z + 456549632 z^2 + 8753152 z^3) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] - 2 Sqrt[z] (3802168755 + 1264664016 z + 92294400 z^2 + 3174400 z^3) 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]