Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9131)

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`=-11/2

http://functions.wolfram.com/07.22.03.9131.01

Input Form

HypergeometricPFQ[{-(19/4)}, {-(11/2), 9/4}, -z] == (1/(4185579847680 z^(5/4))) (Sqrt[Pi] (897189175575 + 3190005957600 z - 1849278816000 z^2 + 296626176000 z^3 - 21572812800 z^4 + 836763648 z^5 - 16777216 z^6) FresnelC[(2 z^(1/4))/Sqrt[Pi]] + 2 z^(1/4) ((-(897189175575 + 140214246480 z - 20030814720 z^2 + 1401200640 z^3 - 53280768 z^4 + 1048576 z^5)) Cos[2 Sqrt[z]] + 4 Sqrt[z] (-299063058525 + 119774183760 z - 18816053760 z^2 + 1358536704 z^3 - 52494336 z^4 + 1048576 z^5) Sin[2 Sqrt[z]]))

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]