Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8c6)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8c6.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 5/4}, z] == (1/(16242969600 z^(9/2))) ((638512875 - 638512875 E^(4 Sqrt[z]) + 1277025750 Sqrt[z] + 1277025750 E^(4 Sqrt[z]) Sqrt[z] + 813928500 z - 813928500 E^(4 Sqrt[z]) z - 74844000 z^(3/2) - 74844000 E^(4 Sqrt[z]) z^(3/2) - 202078800 z^2 + 202078800 E^(4 Sqrt[z]) z^2 + 149688000 z^(5/2) + 149688000 E^(4 Sqrt[z]) z^(5/2) + 13305600 z^3 - 13305600 E^(4 Sqrt[z]) z^3 - 372556800 z^(7/2) - 372556800 E^(4 Sqrt[z]) z^(7/2) + 2980454400 z^4 - 2980454400 E^(4 Sqrt[z]) z^4 + 784464120 z^(9/2) + 784464120 E^(4 Sqrt[z]) z^(9/2) - 3452438880 z^5 + 3452438880 E^(4 Sqrt[z]) z^5 - 117590400 z^(11/2) - 117590400 E^(4 Sqrt[z]) z^(11/2) + 482096640 z^6 - 482096640 E^(4 Sqrt[z]) z^6 + 4024320 z^(13/2) + 4024320 E^(4 Sqrt[z]) z^(13/2) - 16195584 z^7 + 16195584 E^(4 Sqrt[z]) z^7 - 32768 z^(15/2) - 32768 E^(4 Sqrt[z]) z^(15/2) + 131072 z^8 - 131072 E^(4 Sqrt[z]) z^8 + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (1740902625 - 1768536000 z + 242542080 z^2 - 8110080 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(17/4) (1740902625 - 1768536000 z + 242542080 z^2 - 8110080 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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<msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2980454400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 372556800 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 372556800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 13305600 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 13305600 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 149688000 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ 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<apply> <times /> <cn type='integer'> 131072 </cn> <apply> <power /> <ci> z </ci> <cn type='integer'> 8 </cn> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32768 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> -1 </cn> <apply> <times /> <cn type='integer'> 32768 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 15 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <times /> <cn type='integer'> 16195584 </cn> <apply> <power /> <exponentiale /> <apply> <times /> <cn type='integer'> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> </apply> <apply> <power /> <ci> z </ci> <cn type='integer'> 7 </cn> </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]