DLMF:10.8.E1 (Q3063)

From DRMF
Revision as of 13:43, 29 December 2019 by Admin (talk | contribs) (‎Created a new Item: Wikidata Toolkit example test item creation)
(diff) ← Older revision | Latest revision (diff) | Newer revision → (diff)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.8.E1
No description defined

    Statements

    Y n ( z ) = - ( 1 2 z ) - n π k = 0 n - 1 ( n - k - 1 ) ! k ! ( 1 4 z 2 ) k + 2 π ln ( 1 2 z ) J n ( z ) - ( 1 2 z ) n π k = 0 ( ψ ( k + 1 ) + ψ ( n + k + 1 ) ) ( - 1 4 z 2 ) k k ! ( n + k ) ! , Bessel-Y-Weber 𝑛 𝑧 superscript 1 2 𝑧 𝑛 𝜋 superscript subscript 𝑘 0 𝑛 1 𝑛 𝑘 1 𝑘 superscript 1 4 superscript 𝑧 2 𝑘 2 𝜋 1 2 𝑧 Bessel-J 𝑛 𝑧 superscript 1 2 𝑧 𝑛 𝜋 superscript subscript 𝑘 0 digamma 𝑘 1 digamma 𝑛 𝑘 1 superscript 1 4 superscript 𝑧 2 𝑘 𝑘 𝑛 𝑘 {\displaystyle{\displaystyle Y_{n}\left(z\right)=-\frac{(\tfrac{1}{2}z)^{-n}}{% \pi}\sum_{k=0}^{n-1}\frac{(n-k-1)!}{k!}\left(\tfrac{1}{4}z^{2}\right)^{k}+% \frac{2}{\pi}\ln\left(\tfrac{1}{2}z\right)J_{n}\left(z\right)-\frac{(\tfrac{1}% {2}z)^{n}}{\pi}\sum_{k=0}^{\infty}(\psi\left(k+1\right)+\psi\left(n+k+1\right)% )\frac{(-\tfrac{1}{4}z^{2})^{k}}{k!(n+k)!},}}
    0 references
    DLMF:10.8.E1
    0 references