Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8734)

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`=-3/2

http://functions.wolfram.com/07.22.03.8734.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(3/2), -(3/4)}, z] == (1/(218295 z^(1/4))) (Sqrt[2] ((218295 - 1455300 z - 15135120 z^2 + 56692944 z^3 - 32938752 z^4 + 3354624 z^5 - 65536 z^6) BesselI[1/4, Sqrt[z]]^2 + 12 Sqrt[z] (72765 - 388080 z - 4049430 z^2 + 3762528 z^3 - 412160 z^4 + 8192 z^5) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 4 z (218295 - 873180 z - 8773380 z^2 + 7621824 z^3 - 826368 z^4 + 16384 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]