Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8557)

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`=-11/2

http://functions.wolfram.com/07.22.03.8557.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), 11/4}, -z] == ((-Sqrt[Pi]) (94865309004375 + 122125455270000 z - 234480874118400 z^2 + 59550698188800 z^3 - 6227523993600 z^4 + 353752842240 z^5 - 12331253760 z^6 + 268435456 z^7) FresnelS[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) (4 Sqrt[z] (31621769668125 - 15602979520800 z + 3806440646400 z^2 - 393724477440 z^3 + 22260940800 z^4 - 773849088 z^5 + 16777216 z^6) Cos[2 Sqrt[z]] + (-94865309004375 - 20935792332000 z + 4202676576000 z^2 - 413346447360 z^3 + 22894018560 z^4 - 786432000 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/(334846387814400 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]