Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.2288)

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=-1/2, b_1`>=-11/2

For fixed z and a₁=-1/2, b₁=3

http://functions.wolfram.com/07.22.03.2288.01

Input Form

HypergeometricPFQ[{-(1/2)}, {3, 11/2}, z] == (1/(81920 z^4)) (21 (-4 (2 z (1575 - 1080 z - 2048 z^2 - 1664 z^3 + 256 z^4) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (-4725 + 2400 z + 2656 z^2 + 1536 z^3 - 256 z^4) BesselI[1, 2 Sqrt[z]]) + Pi (-4725 + 4500 z - 7200 z^2 - 9600 z^3 - 6400 z^4 + 1024 z^5) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (4725 - 4500 z + 7200 z^2 + 9600 z^3 + 6400 z^4 - 1024 z^5) BesselI[0, 2 Sqrt[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]