Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0469)

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

For fixed z and a₁=-11/2, b₁=-3/2

http://functions.wolfram.com/07.22.03.0469.01

Input Form

HypergeometricPFQ[{-(11/2)}, {-(3/2), 5}, z] == (1/(1964187225 z^(7/2))) (8 (-2 BesselI[1, 2 Sqrt[z]] (972504225 + 412577550 z - 52390800 z^2 - 37422000 z^3 - 14653440 z^4 - 10497024 z^5 - 52273152 z^6 + 6100032 z^7 - 160256 z^8 + 1024 z^9 + 16 Pi z^(13/2) (-3357585 + 383724 z - 10032 z^2 + 64 z^3) StruveL[0, 2 Sqrt[z]]) + Sqrt[z] BesselI[0, 2 Sqrt[z]] (1945008450 - 147349125 z + 130977000 z^2 + 52390800 z^3 + 26576640 z^4 + 49542912 z^5 - 220907520 z^6 + 24718080 z^7 - 643072 z^8 + 4096 z^9 + 32 Pi z^6 (-3357585 + 383724 z - 10032 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]