Results 21 to 30 of about 316 (101)

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

Some sharp inequalities involving Seiffert and other means and their concise proofs [PDF]

, 2012
In the paper, by establishing the monotonicity of some functions involving the sine and cosine functions, the authors provide concise proofs of some known inequalities and find some new sharp inequalities involving the Seiffert, contra-harmonic ...
Jiang, Wei-Dong, Qi, Feng
core   +1 more source

Diagonal recurrence relations for the Stirling numbers of the first kind [PDF]

, 2015
In the paper, the author presents diagonal recurrence relations for the Stirling numbers of the first kind. As by-products, the author also recovers three explicit formulas for special values of the Bell polynomials of the second kind.Comment: 7 ...
Qi, Feng
core   +3 more sources

Limit formulas for ratios of polygamma functions at their singularities

, 2012
In the paper the author presents limit formulas for ratios of polygamma functions at their singularities.Comment: 4 ...
Qi, Feng
core   +2 more sources

On the composition and neutrix composition of the delta function and powers of the inverse hyperbolic sine function [PDF]

, 2010
Lets F be a distribution in D' and let f be a locally summable function. The composition F(f(x)) of F and f is said to exist and be equal to the distribution h(x) if the limit of the sequence {Fn(f(x))} is equal to h(x), where Fn(x)=F(x)*δn(x) for n=1, 2,
Fisher, Brian, Kilicman, Adem
core   +1 more source

Sharpening and generalizations of Shafer's inequality for the arc tangent function

, 2009
In this paper, we sharpen and generalize Shafer's inequality for the arc tangent function.
Bai-Ni Guo, Feng Qi, Shi-Qin Zhang
core   +4 more sources

On transcendental numbers

, 2014
Transcendental numbers play an important role in many areas of science. This paper contains a short survey on transcendental numbers and some relations among them.
Nichita, Florin F.
core   +2 more sources

Numerical Investigation of Fractional Third-Order Differential Equation Using Quartic B-Spline Functions

Advances in Mathematical Physics
MSC2020 Classification: 39A12, 39B62, 33B10, 26A48, 26A51.
Syeda Alishba Batool, Muhammad Abbas, Madiha Shafiq, Y. S. Hamed, Asnake Birhanu   +4 more
doaj   +1 more source

The monotonicity of ratios involving arc tangent function with applications

Open Mathematics, 2019
In this paper, we investigate the monotonicity of the ...
Yang Zhen-Hang, Tin King-Fung, Gao Qin
doaj   +1 more source

Further results on the neutrix composition of distributions involving the delta function and the function cosh+-1(x1/r+1)$\cosh _ + ^{ - 1}\left( {{x^{1/r}} + 1} \right)$

Demonstratio Mathematica, 2019
The neutrix composition F(f (x)) of a distribution F(x) and a locally summable function f (x) is said to exist and be equal to the distribution h(x) if the neutrix limit of the sequence {Fn(f (x))} is equal to h(x), where Fn(x) = F(x) * δn(x) and {δn(x)}
Fisher Brian, Tas Kenan
doaj   +1 more source