Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0825)

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=-1/2

http://functions.wolfram.com/07.22.03.0825.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(1/2), 2}, z] == (1/31185) (-((1/Sqrt[z]) (BesselI[1, 2 Sqrt[z]] (-8505 - 26424 z - 202032 z^2 + 73692 z^3 - 4736 z^4 + 64 z^5 + Pi z^(5/2) (-218295 + 74844 z - 4752 z^2 + 64 z^3) StruveL[0, 2 Sqrt[z]]))) + BesselI[0, 2 Sqrt[z]] (8 (2835 + 10872 z - 59040 z^2 + 19005 z^3 - 1192 z^4 + 16 z^5) + Pi z^2 (-218295 + 74844 z - 4752 z^2 + 64 z^3) 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]