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

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=13/4, b_1`>=-11/2

For fixed z and a₁=13/4, b_1`=11/2

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

Input Form

HypergeometricPFQ[{13/4}, {11/2, -(21/4)}, z] == (1/(2545920 Sqrt[2] z^(15/4))) ((4 z (4036635828225 + 1005462404100 z + 93402771840 z^2 + 3976427520 z^3 + 71925760 z^4 + 262144 z^5) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (12109907484675 + 5323036257000 z + 734932336320 z^2 + 44583229440 z^3 + 1251655680 z^4 + 12058624 z^5) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + (36329722454025 + 22889055905100 z + 4887054239760 z^2 + 423087598080 z^3 + 17237237760 z^4 + 300023808 z^5 + 1048576 z^6) 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]