Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1651)

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=7/2

http://functions.wolfram.com/07.22.03.1651.01

Input Form

HypergeometricPFQ[{-(5/2)}, {7/2, 6}, z] == (1/(4324320 z^(9/2))) (-4 (2 Sqrt[z] (-518400 + 388800 z - 1123200 z^2 - 1198575 z^3 - 1399680 z^4 + 473952 z^5 - 24064 z^6 + 256 z^7) BesselI[0, 2 Sqrt[z]] + (1036800 - 259200 z + 1771200 z^2 + 1579725 z^3 + 1182600 z^4 - 462144 z^5 + 23936 z^6 - 256 z^7) BesselI[1, 2 Sqrt[z]]) + Pi z^(5/2) (-6081075 - 5791500 z - 5148000 z^2 + 1872000 z^3 - 96000 z^4 + 1024 z^5) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(5/2) (6081075 + 5791500 z + 5148000 z^2 - 1872000 z^3 + 96000 z^4 - 1024 z^5) 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]