Wyszukiwarka
Wyniki wyszukiwania dla: DILOGARITHM
Znaleźliśmy mało wyników, wypróbuj alternatywnej metody wyszukiwania.
Filtry
wszystkich: 1
Wyniki wyszukiwania dla: DILOGARITHM
-
On the derivatives $\partial^{2}P_{\nu}(z)/\partial\nu^{2}$ and $\partial Q_{\nu}(z)/\partial\nu$ of the Legendre functions with respect to their degrees
PublikacjaWe provide closed-form expressions for the degree-derivatives $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$ and $[\partial Q_{\nu}(z)/\partial\nu]_{\nu=n}$, with $z\in\mathbb{C}$ and $n\in\mathbb{N}_{0}$, where $P_{\nu}(z)$ and $Q_{\nu}(z)$ are the Legendre functions of the first and the second kind, respectively. For $[\partial^{2}P_{\nu}(z)/\partial\nu^{2}]_{\nu=n}$, we find that % \begin{displaymath} \frac{\partial^{2}P_{\nu}(z)}{\partial\nu^{2}}\bigg|_{\nu=n} =-2P_{n}(z)\Li_{2}\frac{1-z}{2}+B_{n}(z)\ln\frac{z+1}{2}+C_{n}(z), \end{displaymath} % where...