Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8qo)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8qo.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, -(1/4)}, z] == (1/(99677952 z^(7/2))) ((30405375 - 30405375 E^(4 Sqrt[z]) + 60810750 Sqrt[z] + 60810750 E^(4 Sqrt[z]) Sqrt[z] + 38918880 z - 38918880 E^(4 Sqrt[z]) z - 3243240 z^(3/2) - 3243240 E^(4 Sqrt[z]) z^(3/2) - 8255520 z^2 + 8255520 E^(4 Sqrt[z]) z^2 + 9434880 z^(5/2) + 9434880 E^(4 Sqrt[z]) z^(5/2) - 8985600 z^3 + 8985600 E^(4 Sqrt[z]) z^3 + 9897984 z^(7/2) + 9897984 E^(4 Sqrt[z]) z^(7/2) - 16146432 z^4 + 16146432 E^(4 Sqrt[z]) z^4 + 72351744 z^(9/2) + 72351744 E^(4 Sqrt[z]) z^(9/2) + 2813952 z^5 - 2813952 E^(4 Sqrt[z]) z^5 - 11452416 z^(11/2) - 11452416 E^(4 Sqrt[z]) z^(11/2) - 65536 z^6 + 65536 E^(4 Sqrt[z]) z^6 + 262144 z^(13/2) + 262144 E^(4 Sqrt[z]) z^(13/2) + 1024 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (72657 - 11232 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 1024 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (72657 - 11232 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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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]