Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8536)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=-11/2

http://functions.wolfram.com/07.22.03.8536.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(11/2), -(9/4)}, z] == (1/935550) ((467775 + 467775 E^(4 Sqrt[z]) + 935550 Sqrt[z] - 935550 E^(4 Sqrt[z]) Sqrt[z] + 737100 z + 737100 E^(4 Sqrt[z]) z + 226800 z^(3/2) - 226800 E^(4 Sqrt[z]) z^(3/2) - 10080 z^2 - 10080 E^(4 Sqrt[z]) z^2 + 10080 z^(5/2) - 10080 E^(4 Sqrt[z]) z^(5/2) - 33600 z^3 - 33600 E^(4 Sqrt[z]) z^3 + 1800 z^(7/2) - 1800 E^(4 Sqrt[z]) z^(7/2) - 6816 z^4 - 6816 E^(4 Sqrt[z]) z^4 + 128 z^(9/2) - 128 E^(4 Sqrt[z]) z^(9/2) - 512 z^5 - 512 E^(4 Sqrt[z]) z^5 - 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (16065 + 3360 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (16065 + 3360 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML 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]