#### Abstract

The Hadamard product (denoted by∗) of two power series A(x) =a_{0}+a_{1}x+a_{2}x^{2}+···and B(x) =b_{0}+b_{1}x+b_{2}x^{2}+··· is the power series A(x)∗B(x) =a_{0}b_{0}+a_{1}b_{1}x+a_{2}b_{2}x^{2}+···. Although it is well known that the Hadamard product of two rational functions is also rational, a closed form expression of the Hadamard product of rational functions has not been found. Since any rational power series can be expanded by partial fractions as a polynomial plus a sum of power series of the form 1/(1−ax)^{m+1}, to find the Hadamard product of any two rational power series it is sufficient to find the Hadamard product 1/(1−ax)^{m+1}∗ 1/(1−bx)^{n+1 }= (1 +ax)^{m}∗(1+bx)^{n}/(1−abx)^{m+n+1}.The Hadamard product of negative powers of quadratic polynomials have also been derived.

#### Sponsor Name

Ira M. Gessel

#### Recommended Citation

Kar, Ishan
(2022)
"A New Method To Compute The Hadamard Product Of Two Rational Functions,"
*Rose-Hulman Undergraduate Mathematics Journal*: Vol. 23:
Iss.
1, Article 3.

Available at:
https://scholar.rose-hulman.edu/rhumj/vol23/iss1/3