Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0538)

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=1

http://functions.wolfram.com/07.22.03.0538.01

Input Form

HypergeometricPFQ[{-(11/2)}, {1, 4}, -z] == (1/(119401907625 z^2)) (4 (2 z (108056025 + 15127843500 z + 43142576400 z^2 + 19011412080 z^3 + 2152327680 z^4 + 80369664 z^5 + 1054720 z^6 + 4096 z^7) BesselJ[0, Sqrt[z]]^2 - 2 Sqrt[z] (432224100 + 756392175 z + 31824916200 z^2 + 17522629920 z^3 + 2093788800 z^4 + 79585536 z^5 + 1051648 z^6 + 4096 z^7) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + (864448200 + 1404728325 z + 6051137400 z^2 + 70062272640 z^3 + 35984763360 z^4 + 4225842432 z^5 + 159690752 z^6 + 2105344 z^7 + 8192 z^8) BesselJ[1, Sqrt[z]]^2))

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]