DLMF:10.14.E8 (Q3145)

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DLMF:10.14.E8
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    Statements

    test
    | J n ⁡ ( n ⁢ z ) | ≤ | z n ⁢ exp ⁡ ( n ⁢ ( 1 - z 2 ) 1 2 ) | | 1 + ( 1 - z 2 ) 1 2 | n , Bessel-J 𝑛 𝑛 𝑧 superscript 𝑧 𝑛 𝑛 superscript 1 superscript 𝑧 2 1 2 superscript 1 superscript 1 superscript 𝑧 2 1 2 𝑛 {\displaystyle{\displaystyle|J_{n}\left(nz\right)|\leq\frac{\left|z^{n}\exp% \left(n(1-z^{2})^{\frac{1}{2}}\right)\right|}{\left|1+(1-z^{2})^{\frac{1}{2}}% \right|^{n}},}}
    0 references
    DLMF id
    DLMF:10.14.E8
    0 references
    constraint
    n = 0 , 1 , 2 , … 𝑛 0 1 2 … {\displaystyle{\displaystyle n=0,1,2,\dots}}
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    Symbols used
    Bessel function of the first kind
    test
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2agdec
    0 references
    exponential function
    test
    exp ⁡ z 𝑧 {\displaystyle{\displaystyle\exp\NVar{z}}}
    xml-id
    C4.S2.E19.m2abdec
    0 references
     
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