Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1665)

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=-5/2, b_1`>=-11/2

For fixed z and a₁=-5/2, b₁=9/2

http://functions.wolfram.com/07.22.03.1665.01

Input Form

HypergeometricPFQ[{-(5/2)}, {9/2, 5}, z] == (1/(19768320 z^(7/2))) (-4 (2 Sqrt[z] (-4147200 - 9909675 z - 6885900 z^2 - 6674400 z^3 + 2083968 z^4 - 100096 z^5 + 1024 z^6) BesselI[0, 2 Sqrt[z]] + (8294400 + 13831425 z + 8801100 z^2 + 5715360 z^3 - 2034816 z^4 + 99584 z^5 - 1024 z^6) BesselI[1, 2 Sqrt[z]]) + Pi Sqrt[z] (-30405375 - 48648600 z - 32432400 z^2 - 24710400 z^3 + 8236800 z^4 - 399360 z^5 + 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi Sqrt[z] (30405375 + 48648600 z + 32432400 z^2 + 24710400 z^3 - 8236800 z^4 + 399360 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]