Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9594)

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=-19/4, b_1`>=-11/2

For fixed z and a₁=-19/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.9594.01

Input Form

HypergeometricPFQ[{-(19/4)}, {9/2, -(7/4)}, z] == (1/(255826771200 z^(7/2))) ((206239658625 - 206239658625 E^(4 Sqrt[z]) + 412479317250 Sqrt[z] + 412479317250 E^(4 Sqrt[z]) Sqrt[z] + 282842960400 z - 282842960400 E^(4 Sqrt[z]) z + 15713497800 z^(3/2) + 15713497800 E^(4 Sqrt[z]) z^(3/2) - 48064816800 z^2 + 48064816800 E^(4 Sqrt[z]) z^2 + 29578348800 z^(5/2) + 29578348800 E^(4 Sqrt[z]) z^(5/2) - 15168384000 z^3 + 15168384000 E^(4 Sqrt[z]) z^3 + 7855626240 z^(7/2) + 7855626240 E^(4 Sqrt[z]) z^(7/2) - 4513259520 z^4 + 4513259520 E^(4 Sqrt[z]) z^4 + 3114270720 z^(9/2) + 3114270720 E^(4 Sqrt[z]) z^(9/2) - 2854748160 z^5 + 2854748160 E^(4 Sqrt[z]) z^5 + 4175953920 z^(11/2) + 4175953920 E^(4 Sqrt[z]) z^(11/2) - 17634951168 z^6 + 17634951168 E^(4 Sqrt[z]) z^6 - 324796416 z^(13/2) - 324796416 E^(4 Sqrt[z]) z^(13/2) + 1311768576 z^7 - 1311768576 E^(4 Sqrt[z]) z^7 + 4194304 z^(15/2) + 4194304 E^(4 Sqrt[z]) z^(15/2) - 16777216 z^8 + 16777216 E^(4 Sqrt[z]) z^8 - 65536 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (272745 - 20064 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 65536 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (272745 - 20064 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> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 7855626240 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 15168384000 </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> 15168384000 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 29578348800 </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> <mrow> <mn> 29578348800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 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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]