Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8519)

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`=11/2

http://functions.wolfram.com/07.22.03.8519.01

Input Form

HypergeometricPFQ[{-(23/4)}, {11/2, 21/4}, -z] == (Sqrt[Pi] z^(1/4) (6714321790930869740625 - 16527561331522140900000 z + 14691165628019680800000 z^2 - 9643431796853944320000 z^3 + 15883299430112378880000 z^4 + 4840624588224724992000 z^5 + 368809492436169523200 z^6 + 10570446715591065600 z^7 + 128126626855649280 z^8 + 648024665620480 z^9 + 1099511627776 z^10) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 ((-Sqrt[z]) (-1874527441898790380625 + 1564730408177943930000 z - 917190662595596928000 z^2 + 776080693328726016000 z^3 + 283124042236772352000 z^4 + 22459491538226380800 z^5 + 653292740636835840 z^6 + 7970197654732800 z^7 + 40437117091840 z^8 + 68719476736 z^9) Cos[2 Sqrt[z]] + 4 (604974293629009920000 - 1334121898737197233125 z + 1092823522955055738000 z^2 - 707114783801365632000 z^3 + 943981547856257433600 z^4 + 298468908431563161600 z^5 + 22929904689846681600 z^6 + 659167873377239040 z^7 + 8000348325150720 z^8 + 40488656699392 z^9 + 68719476736 z^10) Sin[2 Sqrt[z]]))/(12570365558714793984000 z^(9/2))

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]