Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8342)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8342.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(11/4)}, z] == (1/(186540354000 z^(3/2))) ((15058768725 - 15058768725 E^(4 Sqrt[z]) + 30117537450 Sqrt[z] + 30117537450 E^(4 Sqrt[z]) Sqrt[z] - 21259438200 z + 21259438200 E^(4 Sqrt[z]) z + 10594584000 z^(3/2) + 10594584000 E^(4 Sqrt[z]) z^(3/2) - 4976294400 z^2 + 4976294400 E^(4 Sqrt[z]) z^2 + 2457423360 z^(5/2) + 2457423360 E^(4 Sqrt[z]) z^(5/2) - 1371310080 z^3 + 1371310080 E^(4 Sqrt[z]) z^3 + 928481280 z^(7/2) + 928481280 E^(4 Sqrt[z]) z^(7/2) - 840499200 z^4 + 840499200 E^(4 Sqrt[z]) z^4 + 1219624960 z^(9/2) + 1219624960 E^(4 Sqrt[z]) z^(9/2) - 5127012352 z^5 + 5127012352 E^(4 Sqrt[z]) z^5 - 86441984 z^(11/2) - 86441984 E^(4 Sqrt[z]) z^(11/2) + 348913664 z^6 - 348913664 E^(4 Sqrt[z]) z^6 + 1048576 z^(13/2) + 1048576 E^(4 Sqrt[z]) z^(13/2) - 4194304 z^7 + 4194304 E^(4 Sqrt[z]) z^7 - 16384 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (316825 - 21344 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 16384 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(21/4) (316825 - 21344 z + 256 z^2) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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⁢ </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> 21259438200 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mrow> <mn> 30117537450 </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> 30117537450 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 15058768725 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> </mrow> <mo> + </mo> <mn> 15058768725 </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'> 23 <sep /> 4 </cn> </apply> </list> 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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]