Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.agf4)

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=23/4, b_1`>=-11/2

For fixed z and a₁=23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.agf4.01

Input Form

HypergeometricPFQ[{23/4}, {-(9/2), 17/4}, z] == -((13 (2 Sqrt[z] (-34219518795 + 25511325840 z + 11831339520 z^2 + 4237516800 z^3 + 693043200 z^4 - 110100480 z^5 + 4194304 z^6) BesselI[1/4, Sqrt[z]]^2 + 3 (57032531325 - 83075343120 z - 51943288320 z^2 - 15023923200 z^3 - 3769958400 z^4 + 221249536 z^5 + 20971520 z^6) BesselI[1/4, Sqrt[z]] BesselI[5/4, Sqrt[z]] + 2 Sqrt[z] (171097593975 + 115782171120 z + 35551802880 z^2 + 8650137600 z^3 + 345047040 z^4 - 130547712 z^5 + 4194304 z^6) BesselI[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/(11325726720 Sqrt[2] z^(11/4)))

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]