Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8963)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8963.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(15/4)}, -z] == ((16 z (40479573015 + 97334104896 z - 34174054656 z^2 + 5293080576 z^3 - 557383680 z^4 + 88080384 z^5 + 4194304 z^6) BesselJ[1/4, Sqrt[z]]^2 - 12 Sqrt[z] (-218081170125 + 277923033360 z - 79808295168 z^2 + 11766730752 z^3 - 1256521728 z^4 + 168820736 z^5 + 8388608 z^6) BesselJ[1/4, Sqrt[z]] BesselJ[5/4, Sqrt[z]] + (-3271217551875 - 1395719488800 z + 2085575143680 z^2 - 621710401536 z^3 + 92562849792 z^4 - 9909043200 z^5 + 1358954496 z^6 + 67108864 z^7) BesselJ[5/4, Sqrt[z]]^2) Gamma[5/4]^2)/ (585533988270 Sqrt[2] z^(5/4))

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]