DLMF:10.60.E1 (Q3776): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.m1dec

Latest revision as of 14:17, 2 January 2020

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DLMF:10.60.E1
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    Statements

    Defining formula
    cos ⁡ w w = - ∑ n = 0 ∞ ( 2 ⁢ n + 1 ) ⁢ 𝗃 n ⁡ ( v ) ⁢ 𝗒 n ⁡ ( u ) ⁢ P n ⁡ ( cos ⁡ α ) , 𝑤 𝑤 superscript subscript 𝑛 0 2 𝑛 1 spherical-Bessel-J 𝑛 𝑣 spherical-Bessel-Y 𝑛 𝑢 shorthand-Legendre-P-first-kind 𝑛 𝛼 {\displaystyle{\displaystyle\frac{\cos w}{w}=-\sum_{n=0}^{\infty}(2n+1)\mathsf% {j}_{n}\left(v\right)\mathsf{y}_{n}\left(u\right)P_{n}\left(\cos\alpha\right),}}
    0 references
    DLMF id
    DLMF:10.60.E1
    0 references
    constraint
    | v ⁢ e ± i ⁢ α | < | u | 𝑣 superscript 𝑒 plus-or-minus 𝑖 𝛼 𝑢 {\displaystyle{\displaystyle|ve^{\pm i\alpha}|<|u|}}
    0 references
    Symbols used
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q11447
    Defining formula
    P ν ⁡ ( z ) = P ν 0 ⁡ ( z ) shorthand-Legendre-P-first-kind 𝜈 𝑧 Legendre-P-first-kind 0 𝜈 𝑧 {\displaystyle{\displaystyle P_{\NVar{\nu}}\left(\NVar{z}\right)=P^{0}_{\nu}% \left(z\right)}}
    xml-id
    C14.S2.SS2.p2.m3adec
    0 references
    spherical Bessel function of the first kind
    Defining formula
    𝗃 n ⁡ ( z ) spherical-Bessel-J 𝑛 𝑧 {\displaystyle{\displaystyle\mathsf{j}_{\NVar{n}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E3.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.m1dec
    0 references
     
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