Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1911)

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=-3/2, b_1`>=-11/2

For fixed z and a₁=-3/2, b₁=1

http://functions.wolfram.com/07.22.03.1911.01

Input Form

HypergeometricPFQ[{-(3/2)}, {1, 11/2}, z] == (1/(524288 z^4)) (7 (4 (2 z (-33075 + 7380 z - 3168 z^2 + 11904 z^3 - 14080 z^4 + 1024 z^5) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (99225 - 4500 z + 4896 z^2 - 5760 z^3 + 13568 z^4 - 1024 z^5) BesselI[1, 2 Sqrt[z]]) + Pi (-99225 + 48600 z - 19440 z^2 + 11520 z^3 - 34560 z^4 + 55296 z^5 - 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi (99225 - 48600 z + 19440 z^2 - 11520 z^3 + 34560 z^4 - 55296 z^5 + 4096 z^6) 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]