Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0865)

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/07.22.03.0865.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1/2, 6}, z] == (1/(130945815 z^(9/2))) (4 (2 (-2 Sqrt[z] (32148900 - 893025 z + 1063125 z^2 - 1190700 z^3 - 5715360 z^4 + 32644224 z^5 - 12449574 z^6 + 982200 z^7 - 21920 z^8 + 128 z^9) BesselI[0, 2 Sqrt[z]] + (64297800 + 30362850 z - 4124925 z^2 + 170100 z^3 + 3175200 z^4 + 27186048 z^5 - 11977074 z^6 + 971352 z^7 - 21856 z^8 + 128 z^9) BesselI[1, 2 Sqrt[z]]) + Pi z^(11/2) (59520825 - 24418800 z + 1953504 z^2 - 43776 z^3 + 256 z^4) BesselI[1, 2 Sqrt[z]] StruveL[0, 2 Sqrt[z]] + Pi z^(11/2) (-59520825 + 24418800 z - 1953504 z^2 + 43776 z^3 - 256 z^4) 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]