Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.1305)

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=-7/2, b_1`>=-11/2

For fixed z and a₁=-7/2, b₁=7/2

http://functions.wolfram.com/07.22.03.1305.01

Input Form

HypergeometricPFQ[{-(7/2)}, {7/2, 5}, z] == (1/(518918400 z^(7/2))) (4 (2 Sqrt[z] (-7257600 + 32659200 z + 64529325 z^2 + 138518100 z^3 - 73680480 z^4 + 6592128 z^5 - 161536 z^6 + 1024 z^7) BesselI[0, 2 Sqrt[z]] - (-14515200 + 58060800 z + 91981575 z^2 + 106766100 z^3 - 70521120 z^4 + 6512256 z^5 - 161024 z^6 + 1024 z^7) BesselI[1, 2 Sqrt[z]]) - Pi z^(3/2) (212837625 + 340540200 z + 486486000 z^2 - 288288000 z^3 + 26208000 z^4 - 645120 z^5 + 4096 z^6) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(3/2) (212837625 + 340540200 z + 486486000 z^2 - 288288000 z^3 + 26208000 z^4 - 645120 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]