Taylor’s Expansion

Richard Courant and Fritz John
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Richard Courant: New York University, Courant Institute of Mathematical Sciences
Fritz John: New York University, Courant Institute of Mathematical Sciences

Chapter 5 in Introduction to Calculus and Analysis, 1989, pp 440-480 from Springer

Abstract: Abstract It was a great triumph in the early years of Calculus when Newton and others discovered that many known functions could be expressed as “polynomials of infinite order” or “power series,” with coefficients formed by elegant transparent laws. The geometrical series for 1/(1 − x) or 1/(1 + x2) 1 $$\frac{1}{{1\; - \;x}} = 1 + x + {x^2} \cdots + {x^n} + \cdots $$ 1a $$\frac{1}{{1 + {x^2}}} = 1 - {x^2} + {x^4} - {x^6} + \cdots + {( - 1)^n}{x^{2n}} + \cdots $$ valid for the open interval |x|

Keywords: Taylor Series; Interpolation Formula; Continuous Derivative; Taylor Formula; Taylor Polynomial (search for similar items in EconPapers)
Date: 1989
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DOI: 10.1007/978-1-4613-8955-2_5

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