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Combinatorial identity obtained by the differentiation of convolution

Authors:

N G Kuznetsov

Institution:

(1) Institute of Problems of Mechanical Engineering RAS, St. Petersburg, Russia

Abstract:

The combinatorial identity

$\sum\limits_{k = m}^n {( - 1)^k } \left( \begin{gathered} n \hfill \\ k \hfill \\ \end{gathered} \right)\left( \begin{gathered} k - 1 \hfill \\ m - 1 \hfill \\ \end{gathered} \right) = ( - 1)^m , 1 \leqslant m \leqslant n$

is established with the help of the differentiation of the convolution of some function with the sine function. Bibliography: 5 titles. __________ Translated from Problemy Matematicheskogo Analiza, No. 36, 2007, pp. 65–67.

Keywords:

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