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- W787591736 abstract "In many problems of engineering and the physical sciences we attempt to write the solutions as infinite series of functions. The simplest series representation is the power series. Given a function f(x) of a real variable x containing a number x0 in its domain of definition, we try to find a power series of the form 1.1.1. $$sum^{infty}_{j=0}{a_{j}(x-x_{0})}^{j}$$ which provides a valid representation of f(x) in the interval I of convergence of the power series. It emerges that if f(x) has uniformly bounded derivatives of all orders at each point in I, the above series is uniquely determined and $$a_{j} = frac{f^{(j)}(x_{0})}{j!}$$ where f(j)(x0) is the j-th derivative of f(x) evaluated at x0- Then the series (1.1.1) is called the Taylor series." @default.
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- W787591736 date "1994-01-01" @default.
- W787591736 modified "2023-10-14" @default.
- W787591736 title "Basic Results in Asymptotics" @default.
- W787591736 doi "https://doi.org/10.1007/978-1-4684-0029-8_1" @default.
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