Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8190)

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`=-1/2

http://functions.wolfram.com/07.22.03.8190.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), -(19/4)}, z] == (1/1309458150) ((654729075 + 654729075 E^(4 Sqrt[z]) + 1309458150 Sqrt[z] - 1309458150 E^(4 Sqrt[z]) Sqrt[z] - 275675400 z - 275675400 E^(4 Sqrt[z]) z + 64864800 z^(3/2) - 64864800 E^(4 Sqrt[z]) z^(3/2) - 17297280 z^2 - 17297280 E^(4 Sqrt[z]) z^2 + 5322240 z^(5/2) - 5322240 E^(4 Sqrt[z]) z^(5/2) - 1935360 z^3 - 1935360 E^(4 Sqrt[z]) z^3 + 860160 z^(7/2) - 860160 E^(4 Sqrt[z]) z^(7/2) - 491520 z^4 - 491520 E^(4 Sqrt[z]) z^4 + 393216 z^(9/2) - 393216 E^(4 Sqrt[z]) z^(9/2) - 524288 z^5 - 524288 E^(4 Sqrt[z]) z^5 + 2097152 z^(11/2) - 2097152 E^(4 Sqrt[z]) z^(11/2) + 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) Erf[Sqrt[2] z^(1/4)] + 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) Erfi[Sqrt[2] z^(1/4)])/E^(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]