Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8075)

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`=-7/2

http://functions.wolfram.com/07.22.03.8075.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(7/2), 9/4}, -z] == (1/(4439251353600 z^(5/4))) (Sqrt[Pi] (498438430875 + 2938163382000 z - 3134040940800 z^2 + 1085382144000 z^3 - 225533952000 z^4 + 48113909760 z^5 + 13505658880 z^6 + 268435456 z^7) FresnelC[(2 z^(1/4))/Sqrt[Pi]] - 2 z^(1/4) ((498438430875 + 186870045600 z - 73124755200 z^2 + 14352629760 z^3 - 2277703680 z^4 - 828375040 z^5 - 16777216 z^6) Cos[2 Sqrt[z]] + 4 Sqrt[z] (166146143625 - 206377567200 z + 70089465600 z^2 - 14356070400 z^3 + 2855731200 z^4 + 840957952 z^5 + 16777216 z^6) 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]