Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7w4)

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=-17/4, b_1`>=-11/2

For fixed z and a₁=-17/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a7w4.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, 3/4}, z] == (1/(144200770560 z^(9/2))) ((-10854718875 + 10854718875 E^(4 Sqrt[z]) - 21709437750 Sqrt[z] - 21709437750 E^(4 Sqrt[z]) Sqrt[z] - 14472958500 z + 14472958500 E^(4 Sqrt[z]) z + 3157736400 z^2 - 3157736400 E^(4 Sqrt[z]) z^2 - 1403438400 z^(5/2) - 1403438400 E^(4 Sqrt[z]) z^(5/2) - 801964800 z^3 + 801964800 E^(4 Sqrt[z]) z^3 + 3207859200 z^(7/2) + 3207859200 E^(4 Sqrt[z]) z^(7/2) - 8554291200 z^4 + 8554291200 E^(4 Sqrt[z]) z^4 + 49039441920 z^(9/2) + 49039441920 E^(4 Sqrt[z]) z^(9/2) + 6835338720 z^5 - 6835338720 E^(4 Sqrt[z]) z^5 - 29311282560 z^(11/2) - 29311282560 E^(4 Sqrt[z]) z^(11/2) - 718824960 z^6 + 718824960 E^(4 Sqrt[z]) z^6 + 2932070400 z^(13/2) + 2932070400 E^(4 Sqrt[z]) z^(13/2) + 19374080 z^7 - 19374080 E^(4 Sqrt[z]) z^7 - 77889536 z^(15/2) - 77889536 E^(4 Sqrt[z]) z^(15/2) - 131072 z^8 + 131072 E^(4 Sqrt[z]) z^8 + 524288 z^(17/2) + 524288 E^(4 Sqrt[z]) z^(17/2) + 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (6700791825 - 3729136320 z + 368309760 z^2 - 9748480 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 8 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (6700791825 - 3729136320 z + 368309760 z^2 - 9748480 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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<mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 49039441920 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 9 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8554291200 </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> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 8554291200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3207859200 </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> 3207859200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> 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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]