Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa66)

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`=-9/2

http://functions.wolfram.com/07.22.03.aa66.01

Input Form

HypergeometricPFQ[{-(5/4)}, {-(9/2), -(19/4)}, z] == (1/(12442815 z^(1/4))) (Sqrt[2] ((12442815 - 25613280 z + 9757440 z^2 + 3451392 z^3 + 311808 z^4 + 8192 z^5) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-4147605 + 3007620 z + 1811040 z^2 + 245056 z^3 + 11264 z^4) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (12442815 + 7567560 z + 1496880 z^2 + 104832 z^3 + 2048 z^4) 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]