Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8930)

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`=5/2

http://functions.wolfram.com/07.22.03.8930.01

Input Form

HypergeometricPFQ[{-(21/4)}, {5/2, 1/4}, z] == (1/(12878313525 z^(1/4))) (Sqrt[2] ((12878313525 - 133776573840 z + 174619711224 z^2 - 48316536576 z^3 + 3630219264 z^4 - 83951616 z^5 + 524288 z^6) BesselI[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-4226985000 + 17148825225 z - 5657577408 z^2 + 444691968 z^3 - 10436608 z^4 + 65536 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + (986792625 + 41250610800 z - 141715367640 z^2 + 45674931456 z^3 - 3567771648 z^4 + 83558400 z^5 - 524288 z^6) 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]