Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9544)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9544.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(9/4)}, z] == ((4 z (-4334247225 + 8622784800 z + 7954387200 z^2 + 2895298560 z^3 + 1302528000 z^4 - 217317376 z^5 + 4194304 z^6) BesselI[-(1/4), Sqrt[z]]^2 - 4 Sqrt[z] (-13002741675 + 7039078200 z + 5039193600 z^2 + 1696573440 z^3 + 586874880 z^4 - 107347968 z^5 + 2097152 z^6) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - (39008225025 - 13687096500 z + 45884361600 z^2 + 35460633600 z^3 + 12575047680 z^4 + 4999348224 z^5 - 865075200 z^6 + 16777216 z^7) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(21803418000 Sqrt[2] z^(7/4))

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]