DLMF:10.56.E2 (Q3766)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.56.E2
No description defined

    Statements

    Defining formula
    sin ⁡ z 2 - 2 ⁢ z ⁢ t z = sin ⁡ z z + ∑ n = 1 ∞ t n n ! ⁢ 𝗒 n - 1 ⁡ ( z ) . superscript 𝑧 2 2 𝑧 𝑡 𝑧 𝑧 𝑧 superscript subscript 𝑛 1 superscript 𝑡 𝑛 𝑛 spherical-Bessel-Y 𝑛 1 𝑧 {\displaystyle{\displaystyle\frac{\sin\sqrt{z^{2}-2zt}}{z}=\frac{\sin z}{z}+% \sum_{n=1}^{\infty}\frac{t^{n}}{n!}\mathsf{y}_{n-1}\left(z\right).}}
    0 references
    DLMF id
    DLMF:10.56.E2
    0 references
    Symbols used
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5aadec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2adec
    0 references
    spherical Bessel function of the second kind
    Defining formula
    𝗒 n ⁡ ( z ) spherical-Bessel-Y 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{y}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E4.m2adec
    0 references
    Q11429
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C10.S1.XMD2.m1adec
    0 references
    Q11426
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C10.S1.XMD6.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3766&oldid=45307"