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  1. Artikel ; Online: Chebyshev series: Derivation and evaluation.

    Reynolds, Robert / Stauffer, Allan

    PloS one

    2023  Band 18, Heft 3, Seite(n) e0282703

    Abstract: In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial ...

    Abstract In this paper we use a contour integral method to derive a bilateral generating function in the form of a double series involving Chebyshev polynomials expressed in terms of the incomplete gamma function. Generating functions for the Chebyshev polynomial are also derived and summarized. Special cases are evaluated in terms of composite forms of both Chebyshev polynomials and the incomplete gamma function.
    Sprache Englisch
    Erscheinungsdatum 2023-03-09
    Erscheinungsland United States
    Dokumenttyp Journal Article
    ZDB-ID 2267670-3
    ISSN 1932-6203 ; 1932-6203
    ISSN (online) 1932-6203
    ISSN 1932-6203
    DOI 10.1371/journal.pone.0282703
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

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  2. Artikel ; Online: Extended Wang sum and associated products.

    Reynolds, Robert / Stauffer, Allan

    PloS one

    2022  Band 17, Heft 10, Seite(n) e0276078

    Abstract: The Wang sum involving the exponential sums of Lerch's Zeta functions is extended to the finite sum of the Huwitz-Lerch Zeta function to derive sums and products involving cosine and tangent trigonometric functions. The general theorem used to derive ... ...

    Abstract The Wang sum involving the exponential sums of Lerch's Zeta functions is extended to the finite sum of the Huwitz-Lerch Zeta function to derive sums and products involving cosine and tangent trigonometric functions. The general theorem used to derive these sums and products is in the form of the finite sum over positive integers of the Hurwitz-Lerch Zeta function where the associated parameters are general complex numbers. New Hurwitz-Lerch Zeta function recurrence identities with consecutive neighbours are derived. Some finite sum and product formulae examples involving cosine, tangent and the product of cosine and tangent functions are also derived and evaluated.
    Sprache Englisch
    Erscheinungsdatum 2022-10-17
    Erscheinungsland United States
    Dokumenttyp Journal Article
    ZDB-ID 2267670-3
    ISSN 1932-6203 ; 1932-6203
    ISSN (online) 1932-6203
    ISSN 1932-6203
    DOI 10.1371/journal.pone.0276078
    Datenquelle MEDical Literature Analysis and Retrieval System OnLINE

    Zusatzmaterialien

    Kategorien

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