Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8960)

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/07.22.03.8960.01

Input Form

HypergeometricPFQ[{-(21/4)}, {7/2, -(17/4)}, z] == (-25614965601225 + 25614965601225 E^(4 Sqrt[z]) - 51229931202450 Sqrt[z] - 51229931202450 E^(4 Sqrt[z]) Sqrt[z] - 31623414322500 z + 31623414322500 E^(4 Sqrt[z]) z + 5059746291600 z^(3/2) + 5059746291600 E^(4 Sqrt[z]) z^(3/2) - 879955876800 z^2 + 879955876800 E^(4 Sqrt[z]) z^2 + 167610643200 z^(5/2) + 167610643200 E^(4 Sqrt[z]) z^(5/2) - 35286451200 z^3 + 35286451200 E^(4 Sqrt[z]) z^3 + 8302694400 z^(7/2) + 8302694400 E^(4 Sqrt[z]) z^(7/2) - 2214051840 z^4 + 2214051840 E^(4 Sqrt[z]) z^4 + 681246720 z^(9/2) + 681246720 E^(4 Sqrt[z]) z^(9/2) - 247726080 z^5 + 247726080 E^(4 Sqrt[z]) z^5 + 110100480 z^(11/2) + 110100480 E^(4 Sqrt[z]) z^(11/2) - 62914560 z^6 + 62914560 E^(4 Sqrt[z]) z^6 + 50331648 z^(13/2) + 50331648 E^(4 Sqrt[z]) z^(13/2) - 67108864 z^7 + 67108864 E^(4 Sqrt[z]) z^7 + 268435456 z^(15/2) + 268435456 E^(4 Sqrt[z]) z^(15/2) + 268435456 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(31/4) Erf[Sqrt[2] z^(1/4)] - 268435456 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(31/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(53777874870720 z^(5/2))

Standard Form

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MathML Form

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4 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 8302694400 </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> 8302694400 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mrow> <mn> 7 </mn> <mo> / </mo> <mn> 2 </mn> </mrow> </msup> </mrow> <mo> + </mo> <mrow> <mn> 35286451200 </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> 35286451200 </mn> <mo> ⁢ </mo> <msup> <mi> z </mi> <mn> 3 </mn> </msup> </mrow> <mo> + </mo> <mrow> <mn> 167610643200 </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> 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<msqrt> <mi> z </mi> </msqrt> </mrow> </msup> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 31623414322500 </mn> <mo> ⁢ </mo> <mi> z </mi> </mrow> <mo> - </mo> <mrow> <mn> 51229931202450 </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> 51229931202450 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> + </mo> <mrow> <mn> 25614965601225 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> </mrow> <mo> - </mo> <mn> 25614965601225 </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'> 21 <sep /> 4 </cn> </apply> </list> <list> <cn type='rational'> 7 <sep /> 2 </cn> 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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]