Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8c2)

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.a8c2.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, 1/4}, z] == (1/(16242969600 z^(9/2))) ((-10854718875 + 10854718875 E^(4 Sqrt[z]) - 21709437750 Sqrt[z] - 21709437750 E^(4 Sqrt[z]) Sqrt[z] - 15689173500 z + 15689173500 E^(4 Sqrt[z]) z - 2432430000 z^(3/2) - 2432430000 E^(4 Sqrt[z]) z^(3/2) + 2118085200 z^2 - 2118085200 E^(4 Sqrt[z]) z^2 - 239500800 z^(5/2) - 239500800 E^(4 Sqrt[z]) z^(5/2) - 665280000 z^3 + 665280000 E^(4 Sqrt[z]) z^3 + 1064448000 z^(7/2) + 1064448000 E^(4 Sqrt[z]) z^(7/2) - 1490227200 z^4 + 1490227200 E^(4 Sqrt[z]) z^4 + 2789867520 z^(9/2) + 2789867520 E^(4 Sqrt[z]) z^(9/2) - 13495173120 z^5 + 13495173120 E^(4 Sqrt[z]) z^5 - 926484480 z^(11/2) - 926484480 E^(4 Sqrt[z]) z^(11/2) + 3845038080 z^6 - 3845038080 E^(4 Sqrt[z]) z^6 + 48168960 z^(13/2) + 48168960 E^(4 Sqrt[z]) z^(13/2) - 194248704 z^7 + 194248704 E^(4 Sqrt[z]) z^7 - 524288 z^(15/2) - 524288 E^(4 Sqrt[z]) z^(15/2) + 2097152 z^8 - 2097152 E^(4 Sqrt[z]) z^8 + 512 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (-27633375 + 7579440 z - 380160 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 512 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (-27633375 + 7579440 z - 380160 z^2 + 4096 z^3) 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> 1064448000 </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> 1064448000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 665280000 </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> 665280000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 239500800 </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> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> - </mo> 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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]