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On a connection between thePascal,

Vandermonde and Stirling

matrices-II

On a connection between thePascal,

Vandermonde and Stirling

matrices-II

Moawwad El-Mikkawy

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Introduction

Pascal, Vandermonde and Stirlingmatrices are related to each others.

It is shown that the Pascal matrix P is infact the product of a stochastic matrixT by the Vandermonde matrix V . The

matrix T is related to the Stirlingmatrices S 1 and S 2 of the first andsecond kind respectively.

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The main results

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The main results

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The main resultsDefnition 2.1.

If the n values c 1; c2; . . . ; cn are distinct,then the elementary symmetricpolynomials inc1; c2; . . . ; c j-1; c j+1; . . . ; cn are defined by

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Combinatorial identitiesSome combinatorial identities are given in [1]. It is convenient torewrite them after replacing each k by k+1 and each n by n+1 inboth sides to give

The main results

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THANK YOUTHANK YOU