DLMF:10.47.E17 (Q3690)

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DLMF:10.47.E17
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    Statements

    Defining formula
    𝗄 n ⁡ ( - z ) = - 1 2 ⁢ π ⁢ ( 𝗂 n ( 1 ) ⁡ ( z ) + 𝗂 n ( 2 ) ⁡ ( z ) ) . spherical-Bessel-K 𝑛 𝑧 1 2 𝜋 spherical-Bessel-I-1 𝑛 𝑧 spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{n}\left(-z\right)=-\tfrac{1}{2}\pi% \left({\mathsf{i}^{(1)}_{n}}\left(z\right)+{\mathsf{i}^{(2)}_{n}}\left(z\right% )\right).}}
    0 references
    DLMF id
    DLMF:10.47.E17
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    modified spherical Bessel function
    Defining formula
    𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E7.m2addec
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    modified spherical Bessel function
    Defining formula
    𝗂 n ( 2 ) ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E8.m2addec
    0 references
    modified spherical Bessel function
    Defining formula
    𝗄 n ⁡ ( z ) spherical-Bessel-K 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E9.m2acdec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1pdec
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    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1pdec
    0 references
     
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