Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a9o0)

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=-9/4, b_1`>=-11/2

For fixed z and a₁=-9/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a9o0.01

Input Form

HypergeometricPFQ[{-(9/4)}, {11/2, -(1/4)}, z] == (1/(44301312 z^(9/2))) ((-311070375 + 311070375 E^(4 Sqrt[z]) - 622140750 Sqrt[z] - 622140750 E^(4 Sqrt[z]) Sqrt[z] - 495841500 z + 495841500 E^(4 Sqrt[z]) z - 162162000 z^(3/2) - 162162000 E^(4 Sqrt[z]) z^(3/2) + 6486480 z^2 - 6486480 E^(4 Sqrt[z]) z^2 + 7983360 z^(5/2) + 7983360 E^(4 Sqrt[z]) z^(5/2) - 6048000 z^3 + 6048000 E^(4 Sqrt[z]) z^3 + 3870720 z^(7/2) + 3870720 E^(4 Sqrt[z]) z^(7/2) - 2764800 z^4 + 2764800 E^(4 Sqrt[z]) z^4 + 2555904 z^(9/2) + 2555904 E^(4 Sqrt[z]) z^(9/2) - 3735552 z^5 + 3735552 E^(4 Sqrt[z]) z^5 + 15728640 z^(11/2) + 15728640 E^(4 Sqrt[z]) z^(11/2) + 262144 z^6 - 262144 E^(4 Sqrt[z]) z^6 - 1048576 z^(13/2) - 1048576 E^(4 Sqrt[z]) z^(13/2) - 65536 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (-243 + 16 z) Erf[Sqrt[2] z^(1/4)] + 65536 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(23/4) (-243 + 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> <mo> - </mo> <mrow> <mn> 162162000 </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> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 162162000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 3 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 495841500 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 495841500 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 622140750 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 622140750 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 311070375 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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]