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Series that can be differentiated term-wise m times if the function is m-smooth

Journal Name:

  • Mathematica Æterna

Publication Year:

  • 2011

Key Words:

Author NameUniversity of Author
Abstract (2. Language): 
Let f € Cm(—where m > 0 is an integer. An algorithm is proposed for representing f as a convergent series which admits m times term-wise differentiation. This algorithm is illustrated by numerical examples. It can be used, for example, for acceleration of convergence of Fourier series. The algorithm is generalized to the case when f is piecewise-Cm(—function with known positions of finitely many jump discontinuities and the sizes of the jumps and to the case when these positions and the sizes of the jumps are unknown. A jump dis¬continuity point s is a point at which at least one of the quantities dj := f (j)(s — 0) — f (j)(s + 0) = 0, where 0 < j < m.
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  • 3
137-148
  • English

REFERENCES

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