The integrals in Gradshteyn and Rhyzik. Part 1: A family of logarithmic integrals [PDF]
Scientia, Series A: Mathematical Sciences, Vol. 14 (2007), 1-6, 2007 We present the evaluation of a family of logarithmic integrals. This provides a unified proof of several formulas in the classical table of integrals by I. S. Gradshteyn and I. M. Rhyzik.
arxiv
APP accumulates with presynaptic proteins around amyloid plaques: A role for presynaptic mechanisms in Alzheimer's disease? [PDF]
Alzheimers Dement, 2022 Jordà-Siquier T +8 more
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The integrals in Gradshteyn and Ryzhik. Part 3: Combinations of Logarithms and Exponentials [PDF]
arXiv, 2007 We present the evaluation of a family of exponential-logarithmic integrals. These have integrands of the form P(exp(x),ln(x)) where P is a polynomial. The examples presented here appear in sections 4.33, 4.34 and 4.35 in the classical table of integrals by I. Gradshteyn and I. Ryzhik.
arxiv
The integrals in Gradshteyn and Ryzhik. Part 5: Some trigonometric integrals [PDF]
arXiv, 2007 We present evalauations and provide proofs of definite integrals involving the function x^p cos^n x. These formulae are generalizations of 3.761.11 and 3.822.1, among others, in the classical table of integrals by I. S. Gradshteyn and I. M. Ryzhik.
arxiv
New approximation inequalities for circular functions. [PDF]
J Inequal Appl, 2018 Zhu L, Nenezić M.
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Refinements and generalizations of some inequalities of Shafer-Fink's type for the inverse sine function. [PDF]
J Inequal Appl, 2017 Malešević B, Rašajski M, Lutovac T.
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South African nose flies (Diptera, Calliphoridae, Rhiniinae): taxonomy, diversity, distribution and biology. [PDF]
Biodivers Data J, 2023 Thomas-Cabianca A +3 more
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Extensions of the natural approach to refinements and generalizations of some trigonometric inequalities. [PDF]
Adv Differ Equ, 2018 Malešević B +3 more
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Multivariate Bessel functions and multivariate Hankel transforms [PDF]
arXivThe generalization, similarly to exponential multivariate bases in the Fourier transform, of the Bessel functions to many dimensions is offered. Analogously to the Fourier transform property under the differentiation, the similar Hankel transform property is extended to many dimensions.
arxiv