Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8334)

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/07.22.03.8334.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(19/4)}, z] == (7905853580625 - 7905853580625 E^(4 Sqrt[z]) + 15811707161250 Sqrt[z] + 15811707161250 E^(4 Sqrt[z]) Sqrt[z] - 2529873145800 z + 2529873145800 E^(4 Sqrt[z]) z + 439977938400 z^(3/2) + 439977938400 E^(4 Sqrt[z]) z^(3/2) - 83805321600 z^2 + 83805321600 E^(4 Sqrt[z]) z^2 + 17643225600 z^(5/2) + 17643225600 E^(4 Sqrt[z]) z^(5/2) - 4151347200 z^3 + 4151347200 E^(4 Sqrt[z]) z^3 + 1107025920 z^(7/2) + 1107025920 E^(4 Sqrt[z]) z^(7/2) - 340623360 z^4 + 340623360 E^(4 Sqrt[z]) z^4 + 123863040 z^(9/2) + 123863040 E^(4 Sqrt[z]) z^(9/2) - 55050240 z^5 + 55050240 E^(4 Sqrt[z]) z^5 + 31457280 z^(11/2) + 31457280 E^(4 Sqrt[z]) z^(11/2) - 25165824 z^6 + 25165824 E^(4 Sqrt[z]) z^6 + 33554432 z^(13/2) + 33554432 E^(4 Sqrt[z]) z^(13/2) - 134217728 z^7 + 134217728 E^(4 Sqrt[z]) z^7 - 134217728 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) Erf[Sqrt[2] z^(1/4)] - 134217728 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(53164000890000 z^(3/2))

Standard Form

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MathML Form

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15811707161250 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> <mo> - </mo> <mrow> <mn> 7905853580625 </mn> <mo> ⁢ </mo> <msup> <mi> ⅇ </mi> <mrow> <mn> 4 </mn> <mo> ⁢ </mo> <msqrt> <mi> z </mi> </msqrt> </mrow> </msup> </mrow> <mo> + </mo> <mn> 7905853580625 </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> <list> <cn type='rational'> 5 <sep /> 2 </cn> <apply> <times /> <cn type='integer'> -1 </cn> <cn type='rational'> 19 <sep /> 4 </cn> </apply> </list> <ci> z </ci> </apply> <apply> <times /> <apply> <times /> <cn type='integer'> 1 </cn> <apply> <power /> <apply> <times /> <cn type='integer'> 53164000890000 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 3 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> 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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]