Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0787)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For integer and half-integer parameters and fixed z

For fixed z and a₁=-9/2, b_1`>=-11/2

For fixed z and a₁=-9/2, b₁=-5/2

http://functions.wolfram.com/07.22.03.0787.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(5/2), 6}, z] == (1/(654729075 z^(9/2))) (8 ((-BesselI[1, 2 Sqrt[z]]) (-45972927000 - 31414833450 z - 108056025 z^2 - 89302500 z^3 - 7938000 z^4 - 878400 z^5 - 168192 z^6 - 82944 z^7 - 348160 z^8 + 8192 z^9 + 2048 Pi z^(17/2) (-171 + 4 z) StruveL[0, 2 Sqrt[z]]) + 2 Sqrt[z] BesselI[0, 2 Sqrt[z]] (-22986463500 - 4214184975 z + 137525850 z^2 + 14288400 z^3 + 1360800 z^4 + 195840 z^5 + 59904 z^6 + 86016 z^7 - 352256 z^8 + 8192 z^9 + 1024 Pi z^8 (-171 + 4 z) StruveL[1, 2 Sqrt[z]])))

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]