Results 1 to 10 of about 17,495 (203)
Convergent expansions and bounds for the incomplete elliptic integral of the second kind near the logarithmic singularity [PDF]
Mathematics of Computation, 2022 We find two series expansions for Legendre's second incomplete elliptic integral $E(\lambda, k)$ in terms of recursively computed elementary functions. Both expansions converge at every point of the unit square in the $(\lambda, k)$ plane.
D. Karp, Yi Zhang
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Improving estimates for discrete polynomial averages [PDF]
, 2020 For a polynomial $P$ mapping the integers into the integers, define an averaging operator $A_{N} f(x):=\frac{1}{N}\sum_{k=1}^N f(x+P(k))$ acting on functions on the integers.
Han, Rui +4 more
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Basic Hypergeometric Functions as Limits of Elliptic Hypergeometric Functions [PDF]
, 2009 We describe a uniform way of obtaining basic hypergeometric functions as limits of the elliptic beta integral. This description gives rise to the construction of a polytope with a different basic hypergeometric function attached to each face of this ...
Rains, Eric M., van de Bult, Fokko J.
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On the Fourier transform of functions from a Lorentz space L_2,r with a mixed metric
BULLETIN OF THE KARAGANDA UNIVERSITY-MATHEMATICS, 2023 The classical inequalities of Bochkarev play a very important role in harmonic analysis. The meaning of these inequalities lies in the connection between the metric characteristics of functions and the summability of their Fourier coefficients.
N. Tleukhanova +2 more
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MYMathApps Calculus: Maple Plots
Maple Transactions, 2022 I am writing an online Calculus text called MYMathApps Calculus. You can see a sample at https://mymathapps.com/mymacalc-sample/The text is highly interactive and visual.
Philip Yasskin
semanticscholar +1 more source
Tail probability and divergent series [PDF]
, 2020 From mostly a measure-theoretic consideration, we show that for every nonnegative, finite, and L1 function on a given finite measure space there is some nontrivial sequence of real numbers such that the series, obtained from summing over the term-by-term
Yu-Lin Chou
semanticscholar +1 more source
Riemann sums over polytopes [PDF]
, 2006 We show that the Euler-MacLaurin formula for Riemann sums has an n-dimensional analogue in which intervals on the line get replaced by convex polytopes.Comment: 13 ...
Guillemin, Victor, Sternberg, Shlomo
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Matematychni Studii, 2022 In the present work, we study problem related to the approximation of continuous $2\pi$-periodic functions by linear means of their Fourier series. The simplest example of a linear approximation of periodic function is the approximation of this function ...
O. Rovenska
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Thirty-two Goldbach Variations
, 2005 We give thirty-two diverse proofs of a small mathematical gem--the fundamental Euler sum identity zeta(2,1)=zeta(3) =8zeta(\bar 2,1). We also discuss various generalizations for multiple harmonic (Euler) sums and some of their many connections, thereby ...
Abramowitz M. +30 more
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Journal of Inequalities and Applications, 2012 In the present paper we establish new inequalities similar to the extensions of Hilbert’s double-series inequality and also give their integral analogues. Our results provide some new estimates to these types of inequalities.MSC:26D15.
Chang-Jian Zhao, W. Cheung
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