Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9088)

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/07.22.03.9088.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, 15/4}, z] == (-4 (-10864634167296000 - 21729268334592000 Sqrt[z] + 18625087143936000 z + 66222532067328000 z^(3/2) - 5352979943390625 z^2 + 134137428485778900 z^(5/2) - 5893305547474800 z^3 + 144494720987198400 z^(7/2) + 68090514191481600 z^4 - 305489074017254400 z^(9/2) - 13056291023892480 z^5 + 54212435838812160 z^(11/2) + 707715900702720 z^6 - 2872375557488640 z^(13/2) - 14205274030080 z^7 + 57147345862656 z^(15/2) + 109672660992 z^8 - 439495950336 z^(17/2) - 268435456 z^9 + 1073741824 z^(19/2) + E^(4 Sqrt[z]) (10864634167296000 - 21729268334592000 Sqrt[z] - 18625087143936000 z + 66222532067328000 z^(3/2) + 5352979943390625 z^2 + 134137428485778900 z^(5/2) + 5893305547474800 z^3 + 144494720987198400 z^(7/2) - 68090514191481600 z^4 - 305489074017254400 z^(9/2) + 13056291023892480 z^5 + 54212435838812160 z^(11/2) - 707715900702720 z^6 - 2872375557488640 z^(13/2) + 14205274030080 z^7 + 57147345862656 z^(15/2) - 109672660992 z^8 - 439495950336 z^(17/2) + 268435456 z^9 + 1073741824 z^(19/2))) - E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (361299089805278625 + 600601084351632000 z + 747414682748697600 z^2 - 1258803676208332800 z^3 + 218922378471014400 z^4 - 11531713763082240 z^5 + 228917394800640 z^6 - 1758789107712 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(7/4) (361299089805278625 + 600601084351632000 z + 747414682748697600 z^2 - 1258803676208332800 z^3 + 218922378471014400 z^4 - 11531713763082240 z^5 + 228917394800640 z^6 - 1758789107712 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (5360921109489254400 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]