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DLMF:10.14.E3 - MaRDI portal

DLMF:10.14.E3 (Q3838)

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DLMF:10.14.E3
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    Statements

    DLMF defining formula
    | J n ⁡ ( z ) | ≤ e | ℑ ⁡ z | , Bessel-J 𝑛 𝑧 superscript 𝑒 𝑧 {\displaystyle{\displaystyle|J_{n}\left(z\right)|\leq e^{|\Im z|},}}
    0 references
    constraint
    n ∈ ℤ 𝑛 {\displaystyle{\displaystyle n\in\mathbb{Z}}}
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    Symbols used
    Bessel function of the first kind
    DLMF defining formula
    J ν ⁡ ( z ) Bessel-J 𝜈 𝑧 {\displaystyle{\displaystyle J_{\NVar{\nu}}\left(\NVar{z}\right)}}
    xml-id
    C10.S2.E2.m2abdec
    0 references
    Q10758
    DLMF defining formula
    ∈ {\displaystyle{\displaystyle\in}}
    xml-id
    introduction.Sx4.p1.t1.r10.m2aadec
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    base of natural logarithm
    DLMF defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
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    imaginary part
    DLMF defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
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    Q10792
    DLMF defining formula
    ℤ {\displaystyle{\displaystyle\mathbb{Z}}}
    xml-id
    introduction.Sx4.p2.t1.r20.m2adec
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    integer
    DLMF defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1dec
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    complex variable
    DLMF defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1dec
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    Identifiers

     
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