Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9191)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=-9/2

http://functions.wolfram.com/07.22.03.9191.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 21/4}, -z] == (221 (Sqrt[Pi] (1708405198400525625 + 540682084768518000 z + 124027431631488000 z^2 + 34298944056115200 z^3 + 35790202493337600 z^4 - 10046372629708800 z^5 + 1020583886192640 z^6 - 57837103349760 z^7 + 2203318222848 z^8 - 68719476736 z^9) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-1708405198400525625 + 1281616793525376000 z - 10105938873676800 z^2 + 3308989036953600 z^3 - 707843458990080 z^4 + 67825418895360 z^5 - 3759774105600 z^6 + 141733920768 z^7 - 4294967296 z^8) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-569468399466841875 + 80101049595336000 z - 1026104773478400 z^2 - 2396895904972800 z^3 + 641823220039680 z^4 - 64531652935680 z^5 + 3642400702464 z^6 - 138512695296 z^7 + 4294967296 z^8) Sin[2 Sqrt[z]])))/ (8378806369234452480 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]