Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.aa4a)

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=-7/4, b_1`>=-11/2

For fixed z and a₁=-7/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.aa4a.01

Input Form

HypergeometricPFQ[{-(7/4)}, {11/2, 9/4}, z] == (1/(3394560 z^(9/2))) ((-297675 + 297675 E^(4 Sqrt[z]) - 595350 Sqrt[z] - 595350 E^(4 Sqrt[z]) Sqrt[z] - 359100 z + 359100 E^(4 Sqrt[z]) z + 75600 z^(3/2) + 75600 E^(4 Sqrt[z]) z^(3/2) + 75600 z^2 - 75600 E^(4 Sqrt[z]) z^2 - 161280 z^(5/2) - 161280 E^(4 Sqrt[z]) z^(5/2) + 483840 z^3 - 483840 E^(4 Sqrt[z]) z^3 - 209160 z^(7/2) - 209160 E^(4 Sqrt[z]) z^(7/2) + 1011360 z^4 - 1011360 E^(4 Sqrt[z]) z^4 + 65280 z^(9/2) + 65280 E^(4 Sqrt[z]) z^(9/2) - 267264 z^5 + 267264 E^(4 Sqrt[z]) z^5 - 2048 z^(11/2) - 2048 E^(4 Sqrt[z]) z^(11/2) + 8192 z^6 - 8192 E^(4 Sqrt[z]) z^6 + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (187425 + 529200 z - 134400 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (187425 + 529200 z - 134400 z^2 + 4096 z^3) 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]