Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7982)

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`=-11/2

http://functions.wolfram.com/07.22.03.7982.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(11/2), 13/4}, z] == (-4 z^(1/4) (9595438232774625 + 12793917643699500 Sqrt[z] + 2311159316281200 z - 4716651665880000 z^(3/2) + 581324599215360 z^2 - 1972891895546880 z^(5/2) + 78286345482240 z^3 - 291278022819840 z^(7/2) + 5852797009920 z^4 - 22448623583232 z^(9/2) + 279111008256 z^5 - 1085137747968 z^(11/2) + 9512681472 z^6 - 37245419520 z^(13/2) + 268435456 z^7 - 1073741824 z^(15/2) + E^(4 Sqrt[z]) (9595438232774625 - 12793917643699500 Sqrt[z] + 2311159316281200 z + 4716651665880000 z^(3/2) + 581324599215360 z^2 + 1972891895546880 z^(5/2) + 78286345482240 z^3 + 291278022819840 z^(7/2) + 5852797009920 z^4 + 22448623583232 z^(9/2) + 279111008256 z^5 + 1085137747968 z^(11/2) + 9512681472 z^6 + 37245419520 z^(13/2) + 268435456 z^7 + 1073741824 z^(15/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (9595438232774625 - 7923974798678400 z + 16434910693555200 z^2 + 7621987568025600 z^3 + 1146163544064000 z^4 + 88914505236480 z^5 + 4311006314496 z^6 + 148176371712 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (9595438232774625 - 7923974798678400 z + 16434910693555200 z^2 + 7621987568025600 z^3 + 1146163544064000 z^4 + 88914505236480 z^5 + 4311006314496 z^6 + 148176371712 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(80005963595120640 z^(9/4))

Standard Form

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MathML Form

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type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 7923974798678400 </cn> <ci> z </ci> </apply> </apply> <cn type='integer'> 9595438232774625 </cn> </apply> <apply> <ci> Erf </ci> <apply> <times /> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 2 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 2 </cn> <pi /> </apply> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <plus /> <apply> <times /> <cn type='integer'> 4294967296 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 148176371712 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> 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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]