Taylor series
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1—10 of 18 matching pages
1: 5.7 Series Expansions
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§5.7(i) Maclaurin and Taylor Series
… ►For 15D numerical values of see Abramowitz and Stegun (1964, p. 256), and for 31D values see Wrench (1968). ►
5.7.3
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2: 3.7 Ordinary Differential Equations
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§3.7(ii) Taylor-Series Method: Initial-Value Problems
… ►§3.7(iii) Taylor-Series Method: Boundary-Value Problems
… ►It will be observed that the present formulation of the Taylor-series method permits considerable parallelism in the computation, both for initial-value and boundary-value problems. … ►General methods for boundary-value problems for ordinary differential equations are given in Ascher et al. (1995). … ►The method consists of a set of rules each of which is equivalent to a truncated Taylor-series expansion, but the rules avoid the need for analytic differentiations of the differential equation. …3: 9.19 Approximations
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Corless et al. (1992) describe a method of approximation based on subdividing into a triangular mesh, with values of , stored at the nodes. and are then computed from Taylor-series expansions centered at one of the nearest nodes. The Taylor coefficients are generated by recursion, starting from the stored values of , at the node. Similarly for , .
4: 1.10 Functions of a Complex Variable
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►The right-hand side is the Taylor series for
at
, and its radius of convergence is at least .
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►An analytic function has a zero of order (or multiplicity) () at if the first nonzero coefficient in its Taylor series at is that of .
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►This singularity is removable if for all , and in this case the Laurent series becomes the Taylor series.
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5: 1.5 Calculus of Two or More Variables
6: 2.10 Sums and Sequences
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2.10.25
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►What is the asymptotic behavior of as or ? More specially, what is the behavior of the higher coefficients in a Taylor-series expansion?
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7: 19.19 Taylor and Related Series
§19.19 Taylor and Related Series
…8: Bibliography D
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The Taylor Series.
Oxford University Press, Oxford.
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9: 2.4 Contour Integrals
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►and apply the result of §2.4(iii) to each integral on the right-hand side, the role of the series (2.4.11) being played by the Taylor series of and at .
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10: 2.3 Integrals of a Real Variable
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►We now expand in a Taylor series centered at the peak value of the exponential factor in the integrand:
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