DLMF:10.39.E9 (Q3577): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: modified Bessel function of the first kind / rank
 
Normal rank
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
Defining formula:

I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}

\modBesselI{\NVar{\nu}}@{\NVar{z}}
Property / Symbols used: modified Bessel function of the first kind / qualifier
 
xml-id: C10.S25.E2.m2acdec

Revision as of 13:51, 2 January 2020

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DLMF:10.39.E9
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    Statements

    Defining formula
    I ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν Γ ⁡ ( ν + 1 ) ⁢ F 1 0 ⁡ ( - ; ν + 1 ; 1 4 ⁢ z 2 ) , modified-Bessel-first-kind 𝜈 𝑧 superscript 1 2 𝑧 𝜈 Euler-Gamma 𝜈 1 Gauss-hypergeometric-pFq 0 1 𝜈 1 1 4 superscript 𝑧 2 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=\frac{(\frac{1}{2}z)^{\nu}}% {\Gamma\left(\nu+1\right)}{{}_{0}F_{1}}\left(-;\nu+1;\tfrac{1}{4}z^{2}\right),}}
    0 references
    DLMF id
    DLMF:10.39.E9
    0 references
    Symbols used
    gamma function
    Defining formula
    Γ ⁡ ( z ) Euler-Gamma 𝑧 {\displaystyle{\displaystyle\Gamma\left(\NVar{z}\right)}}
    xml-id
    C5.S2.E1.m2abdec
    0 references
    Q11125
    Defining formula
    F q p ⁡ ( a 1 , … , a p ; b 1 , … , b q ; z ) Gauss-hypergeometric-pFq 𝑝 𝑞 subscript 𝑎 1 … subscript 𝑎 𝑝 subscript 𝑏 1 … subscript 𝑏 𝑞 𝑧 {\displaystyle{\displaystyle{{}_{\NVar{p}}F_{\NVar{q}}}\left(\NVar{a_{1},\dots% ,a_{p}};\NVar{b_{1},\dots,b_{q}};\NVar{z}\right)}}
    xml-id
    C16.S2.m1adec
    0 references
    modified Bessel function of the first kind
    Defining formula
    I ν ⁡ ( z ) modified-Bessel-first-kind 𝜈 𝑧 {\displaystyle{\displaystyle I_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S25.E2.m2acdec
    0 references
     
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