Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8035)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.8035.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(9/2), 17/4}, -z] == (13 (Sqrt[Pi] (86358944094971625 + 44572358242566000 z + 21130599463142400 z^2 + 34298944056115200 z^3 - 14441660655206400 z^4 + 2200634004602880 z^5 - 193995284152320 z^6 + 12669079781376 z^7 - 889058230272 z^8 - 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-86358944094971625 + 47543848792070400 z + 3018657066163200 z^2 - 1075328005570560 z^3 + 151404358533120 z^4 - 12930452029440 z^5 + 828056272896 z^6 - 51539607552 z^7 - 4294967296 z^8) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-28786314698323875 - 1697994599716800 z - 2378335870310400 z^2 + 934411889295360 z^3 - 140145951375360 z^4 + 12285061890048 z^5 - 800474529792 z^6 + 54760833024 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/ (523675398077153280 z^(13/4))

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]