Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0627)

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

For fixed z and a₁=-11/2, b₁=4

http://functions.wolfram.com/07.22.03.0627.01

Input Form

HypergeometricPFQ[{-(11/2)}, {4, 4}, z] == (16 (2 Sqrt[z] (358205722875 + 1239280049700 z + 6293171669400 z^2 - 4939846203600 z^3 + 782850715200 z^4 - 40922910720 z^5 + 826432512 z^6 - 6516736 z^7 + 16384 z^8) BesselI[0, Sqrt[z]]^2 - 4 (358205722875 + 1045737207900 z + 1791785942100 z^2 - 2207089684800 z^3 + 376744615200 z^4 - 20156958720 z^5 + 410786304 z^6 - 3252224 z^7 + 8192 z^8) BesselI[0, Sqrt[z]] BesselI[1, Sqrt[z]] - Sqrt[z] (1906548457275 + 4488982205400 z + 8609627149200 z^2 - 9153475596000 z^3 + 1525978800000 z^4 - 81029062656 z^5 + 1646372864 z^6 - 13017088 z^7 + 32768 z^8) BesselI[1, Sqrt[z]]^2))/(131939107925625 z^(5/2))

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]