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Abstract Let introduce the Sobolev type inner product 〈 f , g 〉 = ∫ 0 ∞ f ( x ) g ( x ) d μ ( x ) + M f ( 0 ) g ( 0 ) + N f ′ ( 0 ) g ′ ( 0 ) , where d μ ( x ) = 1 Γ ( α + 1 ) x α e − x d x , M , N ⩾… (More)

where ! is a weight function, 0, and M; N 0. The location of the zeros of discrete Sobolev orthogonal polynomials is given in terms of the zeros of standard polynomials orthogonal with respect to the… (More)

Let μ be the Laguerre measure supported on the interval [0, ∞), and let δ t be the delta function at a point t. The perturbation dμˆ=(·−ξ)dμ, ξ∉[0, ∞), is the so-called canonical Christofel… (More)

ABSTRACTWe obtain several new results for Neumann series of Bessel functions as well as for its various special cases. The generalization of some well-known results for these kind of series, such as… (More)

Abstract.In this paper we will prove a Cohen type inequality for Fourier expansions in terms of the polynomials orthogonal with respect to the generalized Jacobi weight $$(1 - x)^{\alpha}(1 +… (More)

Let dμ(x) = (1 − x2)α−1/2dx,α> − 1/2, be the Gegenbauer measure on the interval [ − 1, 1] and introduce the non-discrete Sobolev inner product
where λ>0. In this paper we will prove a… (More)

Let introduce the Sobolev-type inner product 〈f, g〉 = Z 1 −1 f(x)g(x)dx + N [f ′(1)g′(1) + f ′(−1)g′(−1)], where N ≥ 0. In this paper we prove a Cohen type inequality for Fourier expansion in terms… (More)

Let introduce the discrete Sobolev-type inner product 〈f, g〉 = ∫ 1 −1 f(x)g(x)dμ(x) + M [f(1)g(1) + f(−1)g(−1)] + N [f ′(1)g′(1) + f ′(−1)g′(−1)],

- Bujar Xh. Fejzullahu
- Proceedings of the Royal Society A: Mathematical…
- 2016

In this paper, we derive a new contour integral representation for the confluent hypergeometric function as well as for its various special cases. Consequently, we derive expansions of the confluent… (More)