Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8088)

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`=-7/2

http://functions.wolfram.com/07.22.03.8088.01

Input Form

HypergeometricPFQ[{-(23/4)}, {-(7/2), 23/4}, z] == ((2 Sqrt[z] (-43693083337700671875 - 35105784707693700000 z + 2519753653216800000 z^2 - 500847419584512000 z^3 + 504317053255680000 z^4 + 204731078462668800 z^5 + 33047425371340800 z^6 + 3672035976806400 z^7 + 480800113950720 z^8 - 83150566850560 z^9 + 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]]^2 + (131079250013102015625 + 305057163666855600000 z + 11809447844594400000 z^2 + 984424238493696000 z^3 - 642997748219904000 z^4 - 227939742174412800 z^5 - 35354356324761600 z^6 - 3845660029747200 z^7 - 430677845606400 z^8 + 82463372083200 z^9 - 1099511627776 z^10) BesselI[-(1/4), Sqrt[z]] BesselI[3/4, Sqrt[z]] - 2 Sqrt[z] (131079250013102015625 + 25421430305571300000 z + 188222562047520000 z^2 - 370653660647424000 z^3 + 566600738173747200 z^4 + 214124653235404800 z^5 + 34020678382387200 z^6 + 3761779318456320 z^7 + 460441968967680 z^8 - 82875688943616 z^9 + 1099511627776 z^10) BesselI[3/4, Sqrt[z]]^2) Gamma[3/4]^2)/(941831567179776000 Sqrt[2] z^(17/4))

Standard Form

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MathML Form

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</cn> <apply> <power /> <ci> z </ci> <cn type='rational'> 1 <sep /> 2 </cn> </apply> </apply> <cn type='integer'> 2 </cn> </apply> </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'> 941831567179776000 </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> </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]