Two‐Point Taylor Expansions of Analytic Functions

By José L. López, N. Temme. 2002

58 citations recorded by the source corpus.

Taylor expansions of analytic functions are considered with respect to two points. Cauchy‐type formulas are given for coefficients and remainders in the expansions, and the regions of convergence are indicated. It is explained how these expansions can be used in deriving uniform asymptotic expansions of integrals. The method is also used for obtaining Laurent expansions in two points.

Subfields: Applied Mathematics, Numerical Analysis, Signal Processing

View Paper: https://www.semanticscholar.org/paper/daff565ce1936de4e0d619cc81b5d52712cd78a6

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In Applied Mathematics

1. Andrea Pascucci
2. Sergio Polidoro

Citations in the corpus

• EXPLICIT IMPLIED VOLATILITIES FOR MULTIFACTOR LOCAL‐STOCHASTIC VOLATILITY MODELS (2013, background): “ = Xn h=0 (h+n−1)! h!n!(n−h)! (−1)hh∂n−h ¯x1 [a(¯x1) −a(¯x 0)] +(−1)n+1n∂n−h ¯x2 [a(¯x2) −a(¯x)] (¯x1 −x¯2)h+n+1 . For the derivation of this result we refer the reader to Estes and Lancaster (1972); Lopez and Temme (2002). Note that truncating the two-point Taylor series expansion (10) at n= mresul”