Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8976)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=7/2

http://functions.wolfram.com/07.22.03.8976.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(1/4)}, z] == (1/(16222586688 z^(5/2))) ((-434188755 + 434188755 E^(4 Sqrt[z]) - 868377510 Sqrt[z] - 868377510 E^(4 Sqrt[z]) Sqrt[z] - 52628940 z + 52628940 E^(4 Sqrt[z]) z + 1052578800 z^(3/2) + 1052578800 E^(4 Sqrt[z]) z^(3/2) - 1804420800 z^2 + 1804420800 E^(4 Sqrt[z]) z^2 + 2790256896 z^(5/2) + 2790256896 E^(4 Sqrt[z]) z^(5/2) - 5646993408 z^3 + 5646993408 E^(4 Sqrt[z]) z^3 + 28737773568 z^(7/2) + 28737773568 E^(4 Sqrt[z]) z^(7/2) + 2662467192 z^4 - 2662467192 E^(4 Sqrt[z]) z^4 - 11272320864 z^(9/2) - 11272320864 E^(4 Sqrt[z]) z^(9/2) - 224606592 z^5 + 224606592 E^(4 Sqrt[z]) z^5 + 913995264 z^(11/2) + 913995264 E^(4 Sqrt[z]) z^(11/2) + 5302272 z^6 - 5302272 E^(4 Sqrt[z]) z^6 - 21307392 z^(13/2) - 21307392 E^(4 Sqrt[z]) z^(13/2) - 32768 z^7 + 32768 E^(4 Sqrt[z]) z^7 + 131072 z^(15/2) + 131072 E^(4 Sqrt[z]) z^(15/2) + 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (15277805361 - 5718009024 z + 458970624 z^2 - 10665984 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 2 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(15/4) (15277805361 - 5718009024 z + 458970624 z^2 - 10665984 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> ⅇ </mi> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <msqrt> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <mi> π </mi> </mrow> </msqrt> <mo> ⁢ </mo> <mrow> <mo> ( </mo> <mrow> <mrow> <mn> 65536 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 4 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 10665984 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 458970624 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 2 </mn> </msup> </mrow> <mo> - </mo> <mrow> <mn> 5718009024 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> + </mo> <mn> 15277805361 </mn> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <mrow> <mi> erf </mi> <mo> ⁡ </mo> <mo> ( </mo> <mrow> <msqrt> <mn> 2 </mn> </msqrt> <mo> ⁢ </mo> <mroot> <mi> z </mi> <mn> 4 </mn> </mroot> </mrow> <mo> ) </mo> </mrow> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 15 </mn> <mo> / </mo> <mn> 4 </mn> </mrow> </msup> </mrow> <mo> - </mo> <mrow> <mn> 2 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> 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<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> 28737773568 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 5646993408 </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> 5646993408 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 2790256896 </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> 2790256896 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 5 </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]