Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9064)

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/07.22.03.9064.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(9/4)}, z] == (-896523796042875 + 896523796042875 E^(4 Sqrt[z]) - 1793047592085750 Sqrt[z] - 1793047592085750 E^(4 Sqrt[z]) Sqrt[z] - 1423053644512500 z + 1423053644512500 E^(4 Sqrt[z]) z - 455377166244000 z^(3/2) - 455377166244000 E^(4 Sqrt[z]) z^(3/2) + 29698510842000 z^2 - 29698510842000 E^(4 Sqrt[z]) z^2 + 29038543934400 z^(5/2) + 29038543934400 E^(4 Sqrt[z]) z^(5/2) - 17413863667200 z^3 + 17413863667200 E^(4 Sqrt[z]) z^3 + 7410154752000 z^(7/2) + 7410154752000 E^(4 Sqrt[z]) z^(7/2) - 2964061900800 z^4 + 2964061900800 E^(4 Sqrt[z]) z^4 + 1228798771200 z^(9/2) + 1228798771200 E^(4 Sqrt[z]) z^(9/2) - 560356392960 z^5 + 560356392960 E^(4 Sqrt[z]) z^5 + 296280391680 z^(11/2) + 296280391680 E^(4 Sqrt[z]) z^(11/2) - 193226342400 z^6 + 193226342400 E^(4 Sqrt[z]) z^6 + 170435543040 z^(13/2) + 170435543040 E^(4 Sqrt[z]) z^(13/2) - 243101859840 z^7 + 243101859840 E^(4 Sqrt[z]) z^7 + 1011867451392 z^(15/2) + 1011867451392 E^(4 Sqrt[z]) z^(15/2) + 13614710784 z^8 - 13614710784 E^(4 Sqrt[z]) z^8 - 54861496320 z^(17/2) - 54861496320 E^(4 Sqrt[z]) z^(17/2) - 134217728 z^9 + 134217728 E^(4 Sqrt[z]) z^9 + 536870912 z^(19/2) + 536870912 E^(4 Sqrt[z]) z^(19/2) + 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(31/4) (487305 - 26208 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 2097152 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(31/4) (487305 - 26208 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(84357450777600 z^(9/2))

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]