Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.7700)

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=6, b₁>=-23/4

For fixed z and a₁=6, b₁=-21/4

http://functions.wolfram.com/07.22.03.7700.01

Input Form

HypergeometricPFQ[{6}, {-(21/4), 21/4}, z] == (1/(1321205760 z^(17/4))) ((8 E^(2 Sqrt[z]) z^(1/4) (-1149049526625 - 524748123900 z - 115848532800 z^2 - 15178363200 z^3 - 1762133760 z^4 - 209280000 z^5 - 3637248 z^6 + 262144 z^7) + E^(4 Sqrt[z]) Sqrt[2 Pi] (1149049526625 - 2298099053250 Sqrt[z] + 2363227366500 z - 1662322662000 z^(3/2) + 900972072000 z^2 - 402615813600 z^(5/2) + 155545790400 z^3 - 54041644800 z^(7/2) + 17911238400 z^4 - 6268838400 z^(9/2) + 2355471360 z^5 - 790179840 z^(11/2) + 181370880 z^6 - 15728640 z^(13/2) - 3932160 z^7 + 1048576 z^(15/2)) Erf[Sqrt[2] z^(1/4)] + Sqrt[2 Pi] (1149049526625 + 2298099053250 Sqrt[z] + 2363227366500 z + 1662322662000 z^(3/2) + 900972072000 z^2 + 402615813600 z^(5/2) + 155545790400 z^3 + 54041644800 z^(7/2) + 17911238400 z^4 + 6268838400 z^(9/2) + 2355471360 z^5 + 790179840 z^(11/2) + 181370880 z^6 + 15728640 z^(13/2) - 3932160 z^7 - 1048576 z^(15/2)) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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</apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 4 </cn> </apply> </apply> </apply> </apply> <apply> <times /> <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'> -1048576 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 3932160 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 15728640 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 181370880 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 6 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 790179840 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 11 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 2355471360 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 5 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 6268838400 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 9 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 17911238400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 4 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 54041644800 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 155545790400 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 3 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 402615813600 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 5 <sep /> 2 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> 900972072000 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 2 </cn> </apply> </apply> <apply> 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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]