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USE OF DERIVATIVES AND DIFFERENTIALS OF VARIOUS ORDERS IN THE EXPANSION OF ENTIRE FUNCTIONS.

  • Dennis M. CatesEmail author
Chapter

Abstract

It is easy to expand an entire function of x into a polynomial ordered according to the ascending powers of this variable, when we know the particular values of the function and of its successive derivatives, for \(x=0.\) In fact, denote by F(x) the given function, by n the degree of this function, and by \( a_0, a_1, a_2, \dots , a_n \) the unknown coefficients of the various powers of x in the expansion we seek, so that we have
$$\begin{aligned} F(x)=a_0 + a_1x + a_2x^2 + \cdots + a_n x^n. \end{aligned}$$

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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.Sun CityUSA

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