DLMF:18.34.E6 (Q6036)

From DRMF
Revision as of 13:29, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:18.34.E6
No description defined

    Statements

    1 2 π i | z | = 1 z a - 2 y n ( z ; a ) y m ( z ; a ) e - 2 / z d z = ( - 1 ) n + a - 1 n !  2 a - 1 ( n + a - 2 ) ! ( 2 n + a - 1 ) δ n , m , 1 2 𝜋 imaginary-unit subscript 𝑧 1 superscript 𝑧 𝑎 2 Bessel-polynomial-y 𝑛 𝑧 𝑎 Bessel-polynomial-y 𝑚 𝑧 𝑎 superscript 𝑒 2 𝑧 𝑧 superscript 1 𝑛 𝑎 1 𝑛 superscript  2 𝑎 1 𝑛 𝑎 2 2 𝑛 𝑎 1 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{|z|=1}z^{a-2}y_{n}% \left(z;a\right)y_{m}\left(z;a\right)e^{-2/z}\mathrm{d}z=\frac{(-1)^{n+a-1}n!% \,2^{a-1}}{(n+a-2)!(2n+a-1)}\delta_{n,m},}}
    0 references
    DLMF:18.34.E6
    0 references
    a = 1 , 2 , 𝑎 1 2 {\displaystyle{\displaystyle a=1,2,\dots}}
    0 references
    y n ( x ; a ) Bessel-polynomial-y 𝑛 𝑥 𝑎 {\displaystyle{\displaystyle y_{\NVar{n}}\left(\NVar{x};\NVar{a}\right)}}
    C18.S34.E1.m2addec
    0 references
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1adec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references