# Leibniz Rules and Their Integral Analogues

Chapter

## Abstract

In this chapter we will consider applications of the generalized convolutions considered in the previous chapter, to obtaining the so-called Leibniz rules and their integral analogues. It is well known that the familiar Leibniz rule for an ordinary derivative operator has the form

$$
\left( {f\left( x \right)g\left( x \right)} \right)^{\left( n \right)} = \sum\limits_{k = 0}^n {\left( {\begin{array}{*{20}c}
n \\
k \\
\end{array} } \right)} \left( {f\left( x \right)} \right)^{\left( k \right)} \left( {g\left( x \right)} \right)^{\left( {n - k} \right)}
$$

(1)

## Keywords

Entire Function Integral Transform Summation Formula Leibniz Rule Previous Chapter
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© Springer Science+Business Media Dordrecht 1994