Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8tz)

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

For fixed z and a₁=-11/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.a8tz.01

Input Form

HypergeometricPFQ[{-(11/4)}, {-(11/2), 21/4}, -z] == (221 (Sqrt[Pi] (1012042268362125 + 223567522794000 z + 34067432044800 z^2 + 5861063577600 z^3 + 3473222860800 z^4 - 483231006720 z^5 + 19377684480 z^6 - 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-1012042268362125 + 855944230125600 z - 69757122758400 z^2 + 588643614720 z^3 - 31399280640 z^4 + 1226833920 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-337347422787375 + 79693457104800 z - 2212170912000 z^2 - 223278612480 z^3 + 30435901440 z^4 - 1214251008 z^5 + 16777216 z^6) Sin[2 Sqrt[z]])))/ (692692325498880 z^(17/4))

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]