Journal article
Solution of difference equations by use of the τ-method
Journal of approximation theory, v 32(3), pp 211-225
1981
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Abstract
In the field of differential equations, the τ-method introduced by C. Lanczos has generated considerable interest because of its novel philosophy. That is, rather than attempting to solve an exact equation approximately, it solves an approximate equation exactly. The τ-method when applied to differential equations has many striking properties. In this paper, the concept is applied to difference equations. For a model we use the equation satisfied by the reciprocal of the gamma function, 1/
Γ(
z + 1). As a consequence of the analysis, we show how to generate the Taylor series coefficients in the expansion of this function about
z = 0. In particular, a novel technique is provided to compute Euler's constant.
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Details
- Title
- Solution of difference equations by use of the τ-method
- Creators
- Yudell L Luke - University of Missouri–Kansas CityJet Wimp - Drexel UniversityBing Y Ting - The Marley Cooling Tower Company, Mission, Kansas, USA
- Publication Details
- Journal of approximation theory, v 32(3), pp 211-225
- Publisher
- Elsevier
- Resource Type
- Journal article
- Language
- English
- Academic Unit
- Mathematics
- Web of Science ID
- WOS:A1981MR65500004
- Scopus ID
- 2-s2.0-49149136191
- Other Identifier
- 991019312382304721
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- Collaboration types
- Domestic collaboration
- Web of Science research areas
- Mathematics