Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8709)

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`=-5/2

http://functions.wolfram.com/07.22.03.8709.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(5/2), 19/4}, -z] == -((11 (Sqrt[Pi] (5289558781381875 + 2769805325523600 z + 1205901638323200 z^2 + 882751526092800 z^3 - 1629695125094400 z^4 + 579447155589120 z^5 - 137350436880384 z^6 + 72448582090752 z^7 + 5682241732608 z^8 + 68719476736 z^9) FresnelS[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) (4 Sqrt[z] (1763186260460625 + 117240437059200 z + 110168791649280 z^2 - 115356033515520 z^3 + 38913778778112 z^4 - 9298646138880 z^5 + 4463209218048 z^6 + 354334801920 z^7 + 4294967296 z^8) Cos[2 Sqrt[z]] + (-5289558781381875 + 2872390707950400 z + 315618700400640 z^2 - 186466439577600 z^3 + 51519716720640 z^4 - 11660169314304 z^5 + 4210946998272 z^6 + 351113576448 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/(24936923717959680 z^(15/4)))

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]