Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0837)

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/07.22.03.0837.01

Input Form

HypergeometricPFQ[{-(9/2)}, {-(1/2), 5}, z] == (1/(34459425 z^(7/2))) (8 (-2 BesselI[1, 2 Sqrt[z]] (8037225 + 2976750 z - 340200 z^2 - 680400 z^3 - 702720 z^4 - 3999744 z^5 + 763920 z^6 - 29312 z^7 + 256 z^8 + 4 Pi z^(11/2) (-1044225 + 192780 z - 7344 z^2 + 64 z^3) StruveL[0, 2 Sqrt[z]]) + Sqrt[z] BesselI[0, 2 Sqrt[z]] (16074450 - 2083725 z + 1701000 z^2 + 1587600 z^3 + 3674880 z^4 - 17457408 z^5 + 3113664 z^6 - 117760 z^7 + 1024 z^8 + 8 Pi z^5 (-1044225 + 192780 z - 7344 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]