Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8276)

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`=1/2

http://functions.wolfram.com/07.22.03.8276.01

Input Form

HypergeometricPFQ[{-(23/4)}, {1/2, 19/4}, z] == ((2 Sqrt[z] (14244766981570125 + 1138442915610000 z + 2590590101299200 z^2 + 302705553011097600 z^3 - 1318581028896768000 z^4 + 525727746553282560 z^5 - 51778088966553600 z^6 + 1693903963029504 z^7 - 19718194855936 z^8 + 68719476736 z^9) BesselI[-(1/4), Sqrt[z]]^2 + (-42734300944710375 - 68534263519722000 z + 33030023791564800 z^2 + 36268261418188800 z^3 + 1060108672057344000 z^4 - 495993009450516480 z^5 + 50751719960739840 z^6 - 1681695518490624 z^7 + 19675245182976 z^8 - 68719476736 z^9) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (42734300944710375 - 22632245162326800 z + 29144138639616000 z^2 - 108804784254566400 z^3 + 1204601669900697600 z^4 - 513409888938885120 z^5 + 51362188895453184 z^6 - 1689001257861120 z^7 + 19701014986752 z^8 - 68719476736 z^9) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (662067647977881600 Sqrt[2] z^(13/4))

Standard Form

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MathML Form

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<apply> <ci> BesselI </ci> <cn type='rational'> 3 <sep /> 4 </cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </apply> </apply> <apply> <power /> <apply> <ci> Gamma </ci> <cn type='rational'> 3 <sep /> 4 </cn> </apply> <cn type='integer'> 2 </cn> </apply> </apply> <apply> <power /> <apply> <times /> <cn type='integer'> 662067647977881600 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 13 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </apply> </apply> </annotation-xml> </semantics> </math>

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]