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    Bessel Function Zeros

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    jstnjose
    bessel

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    © All Rights Reserved
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    Bessel Function Zeros

    Uploaded by

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    bessel

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    bessel

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    63 views2 pages

    Bessel Function Zeros

    Uploaded by

    jstnjose
    bessel

    Copyright:

    © All Rights Reserved
    Download as PDF, TXT or read online from Scribd
    Download as pdf or txt
    of 2

    10/11/2016

    BesselFunctionZerosfromWolframMathWorld

    SearchMathWorld

    Algebra
    AppliedMathematics
    CalculusandAnalysis
    DiscreteMathematics
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    CalculusandAnalysis>SpecialFunctions>BesselFunctions>
    CalculusandAnalysis>Roots>
    InteractiveEntries>InteractiveDemonstrations>

    Besselfunctions

    THINGSTOTRY:

    BesselFunctionZeros

    Besselfunctions
    125+375

    Geometry

    gcd164,88

    HistoryandTerminology
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    Whentheindex isreal,thefunctions
    ,
    ,
    ,and
    eachhaveaninfinitenumberofrealzeros,all
    ofwhicharesimplewiththepossibleexceptionof
    .Fornonnegative ,the thpositivezerosofthesefunctions
    aredenoted
    ,
    ,
    ,and
    ,respectively,exceptthat
    istypicallycountedasthefirstzeroof
    (AbramowitzandStegun1972,p.370).
    Thefirstfewroots
    oftheBesselfunction
    aregiveninthefollowingtableforsmallnonnegativeinteger
    valuesof and .TheycanbefoundintheWolframLanguageusingthecommandBesselJZero[n,k].

    WolframWebResources
    13,594entries
    Lastupdated:TueSep272016

    Created,developed,and
    nurturedbyEricWeisstein
    atWolframResearch

    2.4048

    3.8317

    5.1356

    6.3802

    5.5201

    7.0156

    8.4172

    9.7610

    3
    4

    8.6537 10.1735

    7.5883

    8.7715

    11.0647 12.3386

    11.6198 13.0152 14.3725 15.7002

    11.7915 13.3237 14.7960 16.2235 17.6160 18.9801

    5 14.9309 16.4706 17.9598 19.4094 20.8269 22.2178


    Thefirstfewroots
    ofthederivativeoftheBesselfunction
    aregiveninthefollowingtableforsmall
    nonnegativeintegervaluesof and .VersionsoftheWolframLanguagepriorto6implementedthesezerosas
    BesselJPrimeZeros[n,k]intheBesselZerospackagewhichisnowavailableforseparatedownload(Wolfram
    Research).NotethatcontrarytoAbramowitzandStegun(1972,p.370),theWolframLanguagedefinesthefirstzero
    of
    tobeapproximately3.8317ratherthanzero.

    3.8317

    1.8412

    3.0542

    7.0156

    5.3314

    6.7061

    3 10.1735

    8.5363

    9.9695

    4 13.3237

    4.2012

    5.3175

    6.4156

    8.0152

    9.2824 10.5199

    11.3459 12.6819 13.9872

    11.7060 13.1704 14.5858 15.9641 17.3128

    5 16.4706 14.8636 16.3475 17.7887 19.1960 20.5755

    SEEALSO:

    BesselFunction,BesselFunctionoftheFirstKind
    REFERENCES:
    Abramowitz,M.andStegun,I.A.(Eds.)."Zeros."9.5inHandbookofMathematicalFunctionswithFormulas,Graphs,and
    MathematicalTables,9thprinting.NewYork:Dover,pp.370374,1972.
    Goodwin,E.T.andStaton,J."Tableof

    ."Quart.J.Mech.Appl.Math.1,220224,1948.

    Olver,F.W.J.(Ed.)."ZerosandAssociatedValues."RoyalSocietyMathematicalTables,Vol.7:BesselFunctions.Cambridge,
    England:CambridgeUniversityPress,1960.
    WolframResearch."WolframLanguage&SystemDocumentationCenter:UpgradingfromNumericalMathBesselZeros."
    http://reference.wolfram.com/language/Compatibility/tutorial/NumericalMath/BesselZeros.html.
    WolframResearch."WolframLibraryArchive:NumericalMathBesselZerosLegacyStandardAddOnPackage."
    library.wolfram.com/infocenter/MathSource/6777.

    ReferencedonWolfram|Alpha:BesselFunctionZeros
    CITETHISAS:
    Weisstein,EricW."BesselFunctionZeros."FromMathWorldAWolframWebResource.
    http://mathworld.wolfram.com/BesselFunctionZeros.html

    WolframWebResources

    http://mathworld.wolfram.com/BesselFunctionZeros.html

    1/2

    10/11/2016

    BesselFunctionZerosfromWolframMathWorld
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