Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9961)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=-1/2

http://functions.wolfram.com/07.22.03.9961.01

Input Form

HypergeometricPFQ[{-(17/4)}, {-(1/2), 23/4}, -z] == -((19 (Sqrt[Pi] (1662432759862875 + 759969261651600 z + 260096431795200 z^2 + 106706228428800 z^3 + 94849980825600 z^4 - 303519938641920 z^5 + 647509202436096 z^6 + 164446781571072 z^7 + 7228429959168 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (554144253287625 + 11835075732480 z^2 + 11291664384000 z^3 - 23356135047168 z^4 + 38716613591040 z^5 + 10194977292288 z^6 + 450971566080 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-1662432759862875 + 1013292348868800 z + 100185292247040 z^2 + 15243746918400 z^3 - 31616660275200 z^4 + 32359764197376 z^5 + 9870237499392 z^6 + 447750340608 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/(6649846324789248 z^(19/4)))

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]