Results 11 to 20 of about 266 (93)
Open Mathematics, 2023 In this study, by virtue of a derivative formula for the ratio of two differentiable functions and with aid of a monotonicity rule, the authors expand a logarithmic expression involving the cosine function into the Maclaurin power series in terms of ...
Li Yan-Fang, Qi Feng
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q-Functions and Distributions, Operational and Umbral Methods
Mathematics, 2021 The use of non-standard calculus means have been proven to be extremely powerful for studying old and new properties of special functions and polynomials.
Giuseppe Dattoli +3 more
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On the Fresnel sine integral and the convolution
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 37, Page 2327-2333, 2003., 2003 The Fresnel sine integral S(x), the Fresnel cosine integral C(x), and the associated functions S+(x), S−(x), C+(x), and C−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel sine integral and its associated functions with x+r, xr are evaluated.
Adem Kılıçman
wiley +1 more source
An explicit formula for derivative polynomials of the tangent function
Acta Universitatis Sapientiae: Mathematica, 2017 In the paper, the authors derive an explicit formula for derivative polynomials of the tangent function, deduce an explicit formula for tangent numbers, pose an open problem about obtaining an alternative and explicit formula for derivative polynomials ...
Qi Feng, Guo Bai-Ni
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On the Fresnel integrals and the convolution
International Journal of Mathematics and Mathematical Sciences, Volume 2003, Issue 41, Page 2635-2643, 2003., 2003 The Fresnel cosine integral C(x), the Fresnel sine integral S(x), and the associated functions C+(x), C−(x), S+(x), and S−(x) are defined as locally summable functions on the real line. Some convolutions and neutrix convolutions of the Fresnel cosine integral and its associated functions with x+r and xr are evaluated.
Adem Kiliçman, Brian Fisher
wiley +1 more source
On some trigonometric power sums
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 3, Page 185-191, 2002., 2002 Using the generating function method, the closed formulas for various power sums of trigonometric functions are established. The computer algebra system Maple is used to carry out the complex calculations.
Hongwei Chen
wiley +1 more source
On the sine integral and the convolution
International Journal of Mathematics and Mathematical Sciences, Volume 30, Issue 6, Page 365-375, 2002., 2002 The sine integral Si(λx) and the cosine integral Ci(λx) and their associated functions Si+(λx), Si−(λx), Ci+(λx), Ci−(λx) are defined as locally summable functions on the real line. Some convolutions of these functions and sin(μx), sin+(μx), and sin−(μx) are found.
Brian Fisher, Fatma Al-Sirehy
wiley +1 more source
A Series Expansion for Integral Powers of Arctangent [PDF]
Integral Transforms and Special Functions Volume 17, Issue 7, 2006, 2004 A new series expansion for the function (arctan(x)/x)^n is developed and some properties of the expansion coefficients are obtained.
arxiv +1 more source
Limit formulas for ratios of polygamma functions at their singularities [PDF]
Feng Qi, Limit formulas for ratios between derivatives of the
gamma and digamma functions at their singularities, Filomat 27 (2013), no. 4,
601--604, 2012 In the paper the author presents limit formulas for ratios of polygamma functions at their singularities.
arxiv +1 more source
On an Umbral point of view to the Gaussian and Gaussian like functions [PDF]
arXiv, 2022 In this note we review the theory of Gaussian functions by exploiting a point of view based on symbolic methods of umbral nature. We introduce quasi-Gaussian functions, which are close to Gaussian distribution but have a longer tail. Their use and their link with hypergeometric function is eventually presented.
arxiv