Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a89e)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.a89e.01

Input Form

HypergeometricPFQ[{-(15/4)}, {7/2, 1/4}, z] == (1/(66830400 z^(5/2))) ((-1403325 + 1403325 E^(4 Sqrt[z]) - 2806650 Sqrt[z] - 2806650 E^(4 Sqrt[z]) Sqrt[z] - 207900 z + 207900 E^(4 Sqrt[z]) z + 3326400 z^(3/2) + 3326400 E^(4 Sqrt[z]) z^(3/2) - 6652800 z^2 + 6652800 E^(4 Sqrt[z]) z^2 + 14676480 z^(5/2) + 14676480 E^(4 Sqrt[z]) z^(5/2) - 77091840 z^3 + 77091840 E^(4 Sqrt[z]) z^3 - 7806240 z^(7/2) - 7806240 E^(4 Sqrt[z]) z^(7/2) + 32845440 z^4 - 32845440 E^(4 Sqrt[z]) z^4 + 568320 z^(9/2) + 568320 E^(4 Sqrt[z]) z^(9/2) - 2297856 z^5 + 2297856 E^(4 Sqrt[z]) z^5 - 8192 z^(11/2) - 8192 E^(4 Sqrt[z]) z^(11/2) + 32768 z^6 - 32768 E^(4 Sqrt[z]) z^6 + 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-10308375 + 4158000 z - 288000 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-10308375 + 4158000 z - 288000 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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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]