DLMF:10.60.E6 (Q3781)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.60.E6
No description defined

    Statements

    Defining formula
    𝗄 n ⁡ ( 2 ⁢ z ) = 1 π ⁢ n ! ⁢ z n + 1 ⁢ ∑ k = 0 n ( - 1 ) k ⁢ 2 ⁢ n - 2 ⁢ k + 1 k ! ⁢ ( 2 ⁢ n - k + 1 ) ! ⁢ 𝗄 n - k 2 ⁡ ( z ) . spherical-Bessel-K 𝑛 2 𝑧 1 𝜋 𝑛 superscript 𝑧 𝑛 1 superscript subscript 𝑘 0 𝑛 superscript 1 𝑘 2 𝑛 2 𝑘 1 𝑘 2 𝑛 𝑘 1 spherical-Bessel-K 𝑛 𝑘 2 𝑧 {\displaystyle{\displaystyle\mathsf{k}_{n}\left(2z\right)=\frac{1}{\pi}n!z^{n+% 1}\sum_{k=0}^{n}(-1)^{k}\frac{2n-2k+1}{k!(2n-k+1)!}{\mathsf{k}_{n-k}^{2}}\left% (z\right).}}
    0 references
    DLMF id
    DLMF:10.60.E6
    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.m2aadec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5abdec
    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.m2aadec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1edec
    0 references
    Q11428
    Defining formula
    k 𝑘 {\displaystyle{\displaystyle k}}
    xml-id
    C10.S1.XMD3.m1bdec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1bdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3781&oldid=45736"