Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a7vo)

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.a7vo.01

Input Form

HypergeometricPFQ[{-(17/4)}, {11/2, -(13/4)}, z] == (-1323439889396625 + 1323439889396625 E^(4 Sqrt[z]) - 2646879778793250 Sqrt[z] - 2646879778793250 E^(4 Sqrt[z]) Sqrt[z] - 2219963685439500 z + 2219963685439500 E^(4 Sqrt[z]) z - 910754332488000 z^(3/2) - 910754332488000 E^(4 Sqrt[z]) z^(3/2) - 126493657290000 z^2 + 126493657290000 E^(4 Sqrt[z]) z^2 + 20238985166400 z^(5/2) + 20238985166400 E^(4 Sqrt[z]) z^(5/2) - 3519823507200 z^3 + 3519823507200 E^(4 Sqrt[z]) z^3 + 670442572800 z^(7/2) + 670442572800 E^(4 Sqrt[z]) z^(7/2) - 141145804800 z^4 + 141145804800 E^(4 Sqrt[z]) z^4 + 33210777600 z^(9/2) + 33210777600 E^(4 Sqrt[z]) z^(9/2) - 8856207360 z^5 + 8856207360 E^(4 Sqrt[z]) z^5 + 2724986880 z^(11/2) + 2724986880 E^(4 Sqrt[z]) z^(11/2) - 990904320 z^6 + 990904320 E^(4 Sqrt[z]) z^6 + 440401920 z^(13/2) + 440401920 E^(4 Sqrt[z]) z^(13/2) - 251658240 z^7 + 251658240 E^(4 Sqrt[z]) z^7 + 201326592 z^(15/2) + 201326592 E^(4 Sqrt[z]) z^(15/2) - 268435456 z^8 + 268435456 E^(4 Sqrt[z]) z^8 + 1073741824 z^(17/2) + 1073741824 E^(4 Sqrt[z]) z^(17/2) + 1073741824 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(35/4) Erf[Sqrt[2] z^(1/4)] - 1073741824 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(35/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(28119150259200 z^(9/2))

Standard Form

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MathML Form

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</msup> </mrow> <mo> + </mo> <mrow> <mn> 670442572800 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 3519823507200 </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> 3519823507200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 20238985166400 </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> 20238985166400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 126493657290000 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </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]