Partial sums of hyper-Bessel function with applications
نویسندگان
چکیده
منابع مشابه
Weighted Divisor Sums and Bessel Function Series
On page 335 in his lost notebook, Ramanujan records without proof an identity involving a finite trigonometric sum and a doubly infinite series of ordinary Bessel functions. We provide the first published proof of this result. The identity yields as corollaries representations of weighted divisor sums, in particular, the summatory function for r2(n), the number of representations of the positiv...
متن کاملBessel Polynomials and the Partial Sums of the Exponential Series
Let e k (x) denote the k-th partial sum of the Maclaurin series for the exponential function. Define the (n + 1) × (n + 1) Hankel determinant by setting Hn(x) = det[e i+j (x)] 0≤i,j≤n. We give a closed form evaluation of this determinant in terms of the Bessel polynomials using the method of recently introduced γ-operators.
متن کاملUltra Bessel sequences in direct sums of Hilbert spaces
In this paper, we establish some new results in ultra Bessel sequences and ultra Bessel sequences of subspaces. Also, we investigate ultra Bessel sequences in direct sums of Hilbert spaces. <span style="font-family: NimbusRomNo9L-Regu; font-size: 11pt; color: #000000; font-s...
متن کاملWeighted Divisor Sums and Bessel Function Series, Iv
Abstract. One fragment (page 335) published with Ramanujan’s lost notebook contains two formulas, each involving a finite trigonometric sum and a doubly infinite series of Bessel functions. The identities are connected with the classical circle and divisor problems, respectively. This paper is devoted to the first identity. First, we obtain a generalization in the setting of Riesz sums. Second,...
متن کاملWeighted divisor sums and Bessel function series, V
Let r2(n) denote the number of representations of n as a sum of two squares. Finding the precise order of magnitude for the error term in the asymptotic formula for ∑ n≤x r2(n) is known as the circle problem. Next, let d(n) denote the number of positive divisors of n. Determining the exact order of magnitude of the error term associated with the asymptotic formula for ∑ n≤x d(n) is the divisor ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Hacettepe Journal of Mathematics and Statistics
سال: 2019
ISSN: 2651-477X
DOI: 10.15672/hujms.470930