Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9183)

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/07.22.03.9183.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(9/2), 13/4}, -z] == (Sqrt[Pi] (13457837633625 + 11165020851600 z + 23300913081600 z^2 - 10901011968000 z^3 + 1661106585600 z^4 - 131790274560 z^5 + 6694109184 z^6 - 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-13457837633625 + 3190005957600 z - 831674269440 z^2 + 113639178240 z^3 - 8691056640 z^4 + 434110464 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-4485945877875 - 1670955501600 z + 705738458880 z^2 - 105577758720 z^3 + 8322220032 z^4 - 421527552 z^5 + 16777216 z^6) Sin[2 Sqrt[z]]))/(28411208663040 z^(9/4))

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]