Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8612)

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`=-9/2

http://functions.wolfram.com/07.22.03.8612.01

Input Form

HypergeometricPFQ[{-(21/4)}, {-(9/2), 19/4}, z] == (11 (4 z^(1/4) (241052750180116875 + 321403666906822500 Sqrt[z] + 161498702049048000 z + 19428415284096000 z^(3/2) - 6550576800768000 z^2 + 5657316327936000 z^(5/2) - 1447540048281600 z^3 + 4497106788679680 z^(7/2) - 226929103994880 z^4 + 823698629591040 z^(9/2) - 19734850437120 z^5 + 74516004864000 z^(11/2) - 1141521776640 z^6 + 4357512757248 z^(13/2) - 54760833024 z^7 + 206158430208 z^(15/2) - 4294967296 z^8 + 17179869184 z^(17/2) + E^(4 Sqrt[z]) (-241052750180116875 + 321403666906822500 Sqrt[z] - 161498702049048000 z + 19428415284096000 z^(3/2) + 6550576800768000 z^2 + 5657316327936000 z^(5/2) + 1447540048281600 z^3 + 4497106788679680 z^(7/2) + 226929103994880 z^4 + 823698629591040 z^(9/2) + 19734850437120 z^5 + 74516004864000 z^(11/2) + 1141521776640 z^6 + 4357512757248 z^(13/2) + 54760833024 z^7 + 206158430208 z^(15/2) + 4294967296 z^8 + 17179869184 z^(17/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (-241052750180116875 + 95624231476410000 z - 30147540958080000 z^2 + 15006775943577600 z^3 + 17150601078374400 z^4 + 3228348438282240 z^5 + 294322364743680 z^6 + 17249662402560 z^7 + 811748818944 z^8 + 68719476736 z^9) Erf[Sqrt[2] z^(1/4)] - E^(2 Sqrt[z]) Sqrt[2 Pi] (-241052750180116875 + 95624231476410000 z - 30147540958080000 z^2 + 15006775943577600 z^3 + 17150601078374400 z^4 + 3228348438282240 z^5 + 294322364743680 z^6 + 17249662402560 z^7 + 811748818944 z^8 + 68719476736 z^9) Erfi[Sqrt[2] z^(1/4)]))/E^(2 Sqrt[z])/ (1196972338462064640 z^(15/4))

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]