DLMF:10.49.E16 (Q3718)

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DLMF:10.49.E16
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    Statements

    test
    𝗄 n ⁡ ( z ) = ( - 1 ) n ⁢ 1 2 ⁢ π ⁢ z n ⁢ ( 1 z ⁢ d d z ) n ⁡ e - z z . spherical-Bessel-K 𝑛 𝑧 superscript 1 𝑛 1 2 𝜋 superscript 𝑧 𝑛 superscript 1 𝑧 derivative 𝑧 𝑛 superscript 𝑒 𝑧 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{n}\left(z\right)=(-1)^{n}\tfrac{1}{2}% \pi z^{n}\left(\frac{1}{z}\frac{\mathrm{d}}{\mathrm{d}z}\right)^{n}\frac{e^{-z% }}{z}.}}
    0 references
    DLMF id
    DLMF:10.49.E16
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    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
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    derivative of $$f$$ with respect to $$x$$
    test
    d f d x derivative 𝑓 𝑥 {\displaystyle{\displaystyle\frac{\mathrm{d}\NVar{f}}{\mathrm{d}\NVar{x}}}}
    xml-id
    C1.S4.E4.m2abdec
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    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2afdec
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    modified spherical Bessel function
    test
    𝗄 n ⁡ ( z ) spherical-Bessel-K 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E9.m2abdec
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    Q11429
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1jdec
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    Q11426
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1ndec
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