Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8s0)

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`=11/2

http://functions.wolfram.com/07.22.03.a8s0.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, -(1/4)}, z] == (1/(1373340672 z^(9/2))) ((-4043914875 + 4043914875 E^(4 Sqrt[z]) - 8087829750 Sqrt[z] - 8087829750 E^(4 Sqrt[z]) Sqrt[z] - 6202696500 z + 6202696500 E^(4 Sqrt[z]) z - 1621620000 z^(3/2) - 1621620000 E^(4 Sqrt[z]) z^(3/2) + 395675280 z^2 - 395675280 E^(4 Sqrt[z]) z^2 + 77837760 z^(5/2) + 77837760 E^(4 Sqrt[z]) z^(5/2) - 144668160 z^3 + 144668160 E^(4 Sqrt[z]) z^3 + 125798400 z^(7/2) + 125798400 E^(4 Sqrt[z]) z^(7/2) - 107827200 z^4 + 107827200 E^(4 Sqrt[z]) z^4 + 112410624 z^(9/2) + 112410624 E^(4 Sqrt[z]) z^(9/2) - 177733632 z^5 + 177733632 E^(4 Sqrt[z]) z^5 + 783286272 z^(11/2) + 783286272 E^(4 Sqrt[z]) z^(11/2) + 25919488 z^6 - 25919488 E^(4 Sqrt[z]) z^6 - 105250816 z^(13/2) - 105250816 E^(4 Sqrt[z]) z^(13/2) - 524288 z^7 + 524288 E^(4 Sqrt[z]) z^7 + 2097152 z^(15/2) + 2097152 E^(4 Sqrt[z]) z^(15/2) + 8192 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (97929 - 12896 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 8192 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (97929 - 12896 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]