Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8232)

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/07.22.03.8232.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(1/2), 23/4}, z] == -(((2 Sqrt[z] (3632415580300381875 + 2214043782278328000 z - 520951478183136000 z^2 + 113985964457164800 z^3 - 973827216772300800 z^4 - 2230122603714969600 z^5 + 3261098809035325440 z^6 - 497747915314298880 z^7 + 20731768483086336 z^8 - 282299610431488 z^9 + 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]]^2 + (-10897246740901145625 - 23247459713922444000 z + 3173068094388192000 z^2 - 1150222004976844800 z^3 + 290146091345510400 z^4 + 827111541886156800 z^5 - 2981716808140062720 z^6 + 485251944189788160 z^7 - 20557178062503936 z^8 + 281612415664128 z^9 - 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] + 2 Sqrt[z] (10897246740901145625 + 369401957257132800 z^2 - 404132055802675200 z^3 + 870438274036531200 z^4 + 1576017426854707200 z^5 - 3144261011138150400 z^6 + 492673222475513856 z^7 - 20661623077208064 z^8 + 282024732524544 z^9 - 1099511627776 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/ (2230122603714969600 Sqrt[2] z^(17/4)))

Standard Form

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MathML Form

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<power /> <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'> 2230122603714969600 </cn> <apply> <power /> <cn type='integer'> 2 </cn> <cn type='rational'> 1 <sep /> 2 </cn> </apply> <apply> <power /> <ci> z </ci> <cn type='rational'> 17 <sep /> 4 </cn> </apply> </apply> <cn type='integer'> -1 </cn> </apply> </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]