Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0845)

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/07.22.03.0845.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1/2, 1}, z] == (1/181440) (-4 (2 (-22680 + 307872 z - 419787 z^2 + 96540 z^3 - 5200 z^4 + 64 z^5) BesselI[0, 2 Sqrt[z]] + Sqrt[z] (-162144 + 375777 z - 93996 z^2 + 5168 z^3 - 64 z^4) BesselI[1, 2 Sqrt[z]]) + Pi z (893025 - 1587600 z + 381024 z^2 - 20736 z^3 + 256 z^4) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z (-893025 + 1587600 z - 381024 z^2 + 20736 z^3 - 256 z^4) 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]