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Leibniz Rules and Their Integral Analogues

  • Semen B. Yakubovich
  • Yurii F. Luchko
Part of the Mathematics and Its Applications book series (MAIA, volume 287)

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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Copyright information

© Springer Science+Business Media Dordrecht 1994

Authors and Affiliations

  • Semen B. Yakubovich
    • 1
  • Yurii F. Luchko
    • 1
  1. 1.Department of Mathematics and MechanicsBeylorussian State UniversityMinsk, ByelorussiaRussia

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