Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9553)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.9553.01

Input Form

HypergeometricPFQ[{-(19/4)}, {7/2, -(1/4)}, -z] == -(((4 z (-532275975 - 5022990000 z + 28402214400 z^2 + 27283549440 z^3 + 3722260480 z^4 + 126550016 z^5 + 1048576 z^6) BesselJ[-(1/4), Sqrt[z]]^ 2 - 4 Sqrt[z] (-1596827925 - 2046151800 z + 8146857600 z^2 + 12578751360 z^3 + 1822464000 z^4 + 62947328 z^5 + 524288 z^6) BesselJ[-(1/4), Sqrt[z]] BesselJ[3/4, Sqrt[z]] + (-4790483775 - 5225982300 z - 25217438400 z^2 + 91287705600 z^3 + 105601950720 z^4 + 14764130304 z^5 + 505151488 z^6 + 4194304 z^7) BesselJ[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(16958214000 Sqrt[2] z^(7/4)))

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]