NDLI: A MACSYMA package for the generation and manipulation of chebyshev series

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A MACSYMA package for the generation and manipulation of chebyshev series

Content Provider	ACM Digital Library
Author	Fateman, R. J. Einwohner, T. H.
Abstract	Techniques for a MACSYMA package for expanding an arbitrary univariate expression as a truncated series in Chebyshev polynomials and manipulating such expansions is described. A data structure is introduced to represent a truncated expansion in a set of orthogonal polynomials. The data structure contains the independent variable, the name of the orthogonal polynomial set, the number of terms retained, and a list of the expansion coefficients. Although we restrict attention here to the set of Chebyshev polynomials as the orthogonal set, extension to other orthogonal polynomials will be done later. A data structure for truncated power series is provided as an alternative.The principal function of the package converts a given expression into the aforementioned data structure. Special cases are the conversion of sums, products, the ratio, or the composition of truncated Chebyshev expansions.Another special case is converting an expression free of truncated Chebyshev expansions. The package generates exact expansion coefficients whenever possible. In addition to well-known Chebyshev expansions, such as for polynomials, we provide new methods for getting exact Chebyshev expansions for reciprocals of polynomials of degree one or two, meromorphic functions, arbitrary powers of a first-degree polynomial, the error-function, and generalized hypergeometric functions.When exact Chebyshev expansions for a function are unknown, or too costly to compute, approximate expansions are performed. Conversion to power series and interpolation between the roots of a Chebyshev polynomial are supported. The Clenshaw method for symbolic Chebyshev expansion of the solution of a linear differential equation whose coefficients are low degree polynomials is implemented in the package.
Starting Page	180
Ending Page	185
Page Count	6
File Format	PDF
ISBN	0897913256
DOI	10.1145/74540.74562
Language	English
Publisher	Association for Computing Machinery (ACM)
Publisher Date	1989-07-17
Publisher Place	New York
Access Restriction	Subscribed
Content Type	Text
Resource Type	Article

Sl.	Authority	Responsibilities	Communication Details
1	Ministry of Education (GoI), Department of Higher Education	Sanctioning Authority	https://www.education.gov.in/ict-initiatives
2	Indian Institute of Technology Kharagpur	Host Institute of the Project: The host institute of the project is responsible for providing infrastructure support and hosting the project	https://www.iitkgp.ac.in
3	National Digital Library of India Office, Indian Institute of Technology Kharagpur	The administrative and infrastructural headquarters of the project	Dr. B. Sutradhar bsutra@ndl.gov.in
4	Project PI / Joint PI	Principal Investigator and Joint Principal Investigators of the project	Dr. B. Sutradhar bsutra@ndl.gov.in Prof. Saswat Chakrabarti will be added soon
5	Website/Portal (Helpdesk)	Queries regarding NDLI and its services	support@ndl.gov.in
6	Contents and Copyright Issues	Queries related to content curation and copyright issues	content@ndl.gov.in
7	National Digital Library of India Club (NDLI Club)	Queries related to NDLI Club formation, support, user awareness program, seminar/symposium, collaboration, social media, promotion, and outreach	clubsupport@ndl.gov.in
8	Digital Preservation Centre (DPC)	Assistance with digitizing and archiving copyright-free printed books	dpc@ndl.gov.in
9	IDR Setup or Support	Queries related to establishment and support of Institutional Digital Repository (IDR) and IDR workshops	idr@ndl.gov.in

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