Some generating functions of modified Jacobi polynomials
نویسندگان
چکیده
منابع مشابه
Generating Functions of Jacobi Polynomials
Multiplicative renormalization method (MRM) for deriving generating functions of orthogonal polynomials is introduced by Asai–Kubo– Kuo. They and Namli gave complete lists of MRM-applicable measures for MRM-factors h(x) = ex and (1 − x)−κ. In this paper, MRM-factors h(x) for which the beta distribution B(p, q) over [0, 1] is MRM-applicable are determined. In other words, all generating function...
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In this note we have obtained some novel result on mixed trilateral relations involving extended Jacobi polynomials by group theoretic method which inturn yields the corresponding results involving Hermite, Laguerre and Jacobi polynomials.
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we find an explicit expression of the tutte polynomial of an $n$-fan. we also find a formula of the tutte polynomial of an $n$-wheel in terms of the tutte polynomial of $n$-fans. finally, we give an alternative expression of the tutte polynomial of an $n$-wheel and then prove the explicit formula for the tutte polynomial of an $n$-wheel.
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A main motivation for this paper is the search for the sufficient condition of the primality of an integer n in order that the congruence 1n−1 + 2n−1 + 3n−1 + · · · + (n− 1)n−1 ≡ −1 (mod n) holds. Some properties of Jacobi polynomials were investigated using certain Kummer results. Certain properties of Bernoulli polynomials as well as the Staudt–Clausen theorem for prime factors were also used...
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ژورنال
عنوان ژورنال: Communications, Faculty Of Science, University of Ankara Series A1Mathematics and Statistics
سال: 1992
ISSN: 1303-5991
DOI: 10.1501/commua1_0000000512