Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8314)

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`=3/2

http://functions.wolfram.com/07.22.03.8314.01

Input Form

HypergeometricPFQ[{-(23/4)}, {3/2, 9/4}, z] == (-4 z^(1/4) (7905853580625 - 156173559210900 Sqrt[z] - 129358925488800 z + 663180061219200 z^(3/2) + 68131481644800 z^2 - 294023789337600 z^(5/2) - 8106056663040 z^3 + 33318118686720 z^(7/2) + 311852728320 z^4 - 1259852267520 z^(9/2) - 4204789760 z^5 + 16869490688 z^(11/2) + 16777216 z^6 - 67108864 z^(13/2) + E^(4 Sqrt[z]) (7905853580625 + 156173559210900 Sqrt[z] - 129358925488800 z - 663180061219200 z^(3/2) + 68131481644800 z^2 + 294023789337600 z^(5/2) - 8106056663040 z^3 - 33318118686720 z^(7/2) + 311852728320 z^4 + 1259852267520 z^(9/2) - 4204789760 z^5 - 16869490688 z^(11/2) + 16777216 z^6 + 67108864 z^(13/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (7905853580625 + 885455601030000 z - 2833457923296000 z^2 + 1199347269120000 z^3 - 134192701440000 z^4 + 5051960524800 z^5 - 67528294400 z^6 + 268435456 z^7) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (7905853580625 + 885455601030000 z - 2833457923296000 z^2 + 1199347269120000 z^3 - 134192701440000 z^4 + 5051960524800 z^5 - 67528294400 z^6 + 268435456 z^7) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(5518544338944000 z^(5/4))

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]