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DLMF:10.46.E2 - MaRDI portal

DLMF:10.46.E2 (Q4364)

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DLMF:10.46.E2
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    Statements

    DLMF defining formula
    I ν ⁡ ( z ) = ( 1 2 ⁢ z ) ν ⁢ ϕ ⁡ ( 1 , ν + 1 ; 1 4 ⁢ z 2 ) . modified-Bessel-first-kind 𝜈 𝑧 superscript 1 2 𝑧 𝜈 generalized-Bessel-function 1 𝜈 1 1 4 superscript 𝑧 2 {\displaystyle{\displaystyle I_{\nu}\left(z\right)=\left(\tfrac{1}{2}z\right)^% {\nu}\phi\left(1,\nu+1;\tfrac{1}{4}z^{2}\right).}}
    0 references
    Symbols used
    generalized Bessel function
    DLMF defining formula
    ϕ ⁡ ( ρ , β ; z ) generalized-Bessel-function 𝜌 𝛽 𝑧 {\displaystyle{\displaystyle\phi\left(\NVar{\rho},\NVar{\beta};\NVar{z}\right)}}
    xml-id
    C10.S46.E1.m2aadec
    0 references
    modified Bessel function of the first kind
    DLMF 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.m2adec
    0 references
    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
    complex parameter
    DLMF defining formula
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    xml-id
    C10.S1.XMD7.m1dec
    0 references

    Identifiers

     
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