Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.afi3)

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`=-9/2

http://functions.wolfram.com/07.22.03.afi3.01

Input Form

HypergeometricPFQ[{19/4}, {-(9/2), -(21/4)}, -z] == (1/683847289125) (5 (136769457825 - 301037536800 z + 151491740400 z^2 - 42591225600 z^3 + 10644480000 z^4 - 5722472448 z^5 - 10717495296 z^6 + 218103808 z^7) Cos[2 Sqrt[z]] - 2 Sqrt[z] (-683847289125 + 593391298500 z - 209416006800 z^2 + 52091424000 z^3 - 14902272000 z^4 + 34290401280 z^5 - 6086983680 z^6 + 16777216 z^7) Sin[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]