note that Chebyshev polynomials of the first and second kinds are odd for odd orders and even for even orders [3]. This means that in the first equation, every term inT2n+ 1has a factor of √(1 +x) that is canceled out by the 1/√(1 +x) term up front. In the second equation...
Product of Sum and Difference of the Same Two Terms:(These binomials differ only by the sign of the second term and are calledbinomial conjugates.) (a + b)(a - b) =a² -b² While there appears to be "no" middle term in this pattern to form a trinomial, the truth is that ...
We evaluate in closed form a large class of power series where the coefficients are products of special numbers, or products of special numbers and Laguerre polynomials. A num-ber of examples is presented involving harmonic, hyperharmonic, Fibonacci, Lucas, Bernoulli, Euler, and derangement numbers...
This paper presents an integral involving the product of the multivariable H-function, Fox's H-function and a general class of polynomials of one variable and multivariable with essentially arbitrary coefficients by assigning suitable values to these coefficients, our result can be reduced to integrals...
Asymmetric Simple Exclusion Process with Open Boundaries and Koornwinder Polynomials Article17 January 2017 A generalized asymmetric exclusion process withstochastic duality ArticleOpen access05 November 2015 1Introduction This paper is devoted to Malte Henkel on the occasion of his 60th birthday. The main...
Irreducibles and the composed product for polynomials over a finite field Discrete Mathematics, 65 (2) (1987), pp. 115-139 View PDFView articleView in ScopusGoogle Scholar Brawley et al., 1999 J.V. Brawley, S. Gao, D. Mills Computing composed products of polynomials Finite Fields: Theory...
The aim of the present work is to obtain the inverse Laplace transform of the product of the factors of the type , a general class of polynomials an the multivariable H-function. The polynomials and the functions involved in our main formula as well as their arguments are quite general in ...
Using the Hadamard factorization, the exponential radii of starlikeness and convexity for various special functions like Wright function, Lommel function, Struve function, Ramanujan type entire function, cross product and product of Bessel function have been investigated. For certain ranges of the paramet...
An important characteristic of the method is that the first groups of subexpressions and the first matrix obtained from the product matrix decomposition are common to any irreducible polynomial, so the method can be generalized to perform the multiplication over general irreducible polynomials. ...
Orthogonal polynomials33C454004As a by-product of his work, E. Symeonidis obtained in ( Comment . Math. Univ. Carol. 44(3):437–460, 2003 ) indirect proofs of two interesting special function identities involving Gegenbauer polynomials. In (Muldoon, 2004 http://staff.science.uva.nl/~thk/...