Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8446)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8446.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(3/4)}, z] == (1/(4056681657600 z^(7/2))) ((677644592625 - 677644592625 E^(4 Sqrt[z]) + 1355289185250 Sqrt[z] + 1355289185250 E^(4 Sqrt[z]) Sqrt[z] + 765339775200 z - 765339775200 E^(4 Sqrt[z]) z - 276372696600 z^(3/2) - 276372696600 E^(4 Sqrt[z]) z^(3/2) - 228947796000 z^2 + 228947796000 E^(4 Sqrt[z]) z^2 + 392481936000 z^(5/2) + 392481936000 E^(4 Sqrt[z]) z^(5/2) - 407018304000 z^3 + 407018304000 E^(4 Sqrt[z]) z^3 + 409155563520 z^(7/2) + 409155563520 E^(4 Sqrt[z]) z^(7/2) - 484147445760 z^4 + 484147445760 E^(4 Sqrt[z]) z^4 + 840042086400 z^(9/2) + 840042086400 E^(4 Sqrt[z]) z^(9/2) - 3926187048960 z^5 + 3926187048960 E^(4 Sqrt[z]) z^5 - 226171825920 z^(11/2) - 226171825920 E^(4 Sqrt[z]) z^(11/2) + 941226617856 z^6 - 941226617856 E^(4 Sqrt[z]) z^6 + 12907917312 z^(13/2) + 12907917312 E^(4 Sqrt[z]) z^(13/2) - 52287160320 z^7 + 52287160320 E^(4 Sqrt[z]) z^7 - 222101504 z^(15/2) - 222101504 E^(4 Sqrt[z]) z^(15/2) + 891551744 z^8 - 891551744 E^(4 Sqrt[z]) z^8 + 1048576 z^(17/2) + 1048576 E^(4 Sqrt[z]) z^(17/2) - 4194304 z^9 + 4194304 E^(4 Sqrt[z]) z^9 - 64 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (63829148625 - 14854783680 z + 819574272 z^2 - 13942784 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 64 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (63829148625 - 14854783680 z + 819574272 z^2 - 13942784 z^3 + 65536 z^4) 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]