Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.0888)

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

http://functions.wolfram.com/07.22.03.0888.01

Input Form

HypergeometricPFQ[{-(9/2)}, {1, 6}, -z] == (1/(41247931725 z^4)) (32 (z (514382400 + 176818950 z + 81265275 z^2 + 1350253800 z^3 + 2570732640 z^4 + 656106624 z^5 + 41317632 z^6 + 789504 z^7 + 4096 z^8) BesselJ[0, Sqrt[z]]^2 - Sqrt[z] (2057529600 + 450084600 z + 225935325 z^2 + 200037600 z^3 + 2140901280 z^4 + 626409216 z^5 + 40732416 z^6 + 786432 z^7 + 4096 z^8) BesselJ[0, Sqrt[z]] BesselJ[1, Sqrt[z]] + (2057529600 + 192893400 z + 158958450 z^2 + 168781725 z^3 + 450084600 z^4 + 2271344256 z^5 + 636027264 z^6 + 40925952 z^7 + 787456 z^8 + 4096 z^9) 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]