Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8qk)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.a8qk.01

Input Form

HypergeometricPFQ[{-(13/4)}, {9/2, -(5/4)}, z] == (1/(498389760 z^(7/2))) ((577702125 - 577702125 E^(4 Sqrt[z]) + 1155404250 Sqrt[z] + 1155404250 E^(4 Sqrt[z]) Sqrt[z] + 827026200 z - 827026200 E^(4 Sqrt[z]) z + 113513400 z^(3/2) + 113513400 E^(4 Sqrt[z]) z^(3/2) - 103783680 z^2 + 103783680 E^(4 Sqrt[z]) z^2 + 51891840 z^(5/2) + 51891840 E^(4 Sqrt[z]) z^(5/2) - 25159680 z^3 + 25159680 E^(4 Sqrt[z]) z^3 + 13547520 z^(7/2) + 13547520 E^(4 Sqrt[z]) z^(7/2) - 8847360 z^4 + 8847360 E^(4 Sqrt[z]) z^4 + 7766016 z^(9/2) + 7766016 E^(4 Sqrt[z]) z^(9/2) - 11010048 z^5 + 11010048 E^(4 Sqrt[z]) z^5 + 45613056 z^(11/2) + 45613056 E^(4 Sqrt[z]) z^(11/2) + 524288 z^6 - 524288 E^(4 Sqrt[z]) z^6 - 2097152 z^(13/2) - 2097152 E^(4 Sqrt[z]) z^(13/2) - 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (-351 + 16 z) Erf[Sqrt[2] z^(1/4)] + 131072 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (-351 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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<mrow> <mn> 577702125 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> </mrow> <mo> + </mo> <mn> 577702125 </mn> </mrow> <mo> ) </mo> </mrow> </mrow> <mo> ) </mo> </mrow> </mrow> </mrow> <annotation-xml encoding='MathML-Content'> <apply> <eq /> <apply> <ci> HypergeometricPFQ </ci> <list> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 13 <sep /> 4 </cn> </apply> </list> <list> <cn type='rational'> 9 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 5 <sep /> 4 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 498389760 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 7 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> <apply> <times /> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> -2 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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]