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Questions related from Feng Qi
Do you know the web sites of the journals Ars Combinatoria and Utilitas Mathematica? Are these two journals ceased? One of my manuscripts was accepted a long time ago for publishing in the first...
07 September 2021 1,733 14 View
Dear Colleagues Could you please photocopy Formula 88.2.2 and Formula 10.49.33 in the following book published in 1975 by Hansen? E. R. Hansen, A Table of Series and Products, Prentice-Hall,...
26 January 2021 381 6 View
In the preprint W.-H. Li and F. Qi, A further generalization of the Catalan numbers and its explicit formula and integral representation, Authorea Preprints (2020), available online at...
25 August 2020 4,635 21 View
How to prove or where to find a proof of the lower Hessenberg determinant showed by two pictures uploaded here?
03 June 2019 7,173 25 View
Is it a variant of Vandermonde convolution formula for falling factorials? What is the answer? See the picture.
01 April 2018 8,215 5 View
Can one explicitly compute the Laplace transform of a function involving the reciprocal of the gamma function? See the picture for the Laplace transform. Thank you very much.
19 September 2017 7,939 10 View
The famous Sylvester matrix was studied in 1854. It is defined as showed in the picture uploaded here. My question is: What and where is the inverse of the Sylvester matrix?
13 July 2017 1,824 9 View
Is the series in the picture convergent? If it is convergent, what is the sum of the series?
22 May 2017 4,988 17 View
Dear All Happy New Year. Can one verify an identity involving factorials? For details, please see the picture uploaded with this message. Best regards Feng Qi (F. Qi) https://qifeng618.wordpress.com
27 December 2016 976 45 View
What are completely monotonic functions on an interval $I$? See the picture 1.png What is the Bernstein-Widder theorem for completely monotonic functions on the infinite interval $I=(0,\infty)$?...
14 July 2016 3,357 12 View
How to find by hand or by software a doubly stochastic matrix? See the picture uploaded with this message. Thank a lot.
11 July 2016 4,787 15 View
Dear Colleagues About computation of the general tridiagonal determinant, I have a guess, see the PNG or PDF files uploaded with this message. Could you please supply a proof for (verify) the...
19 June 2016 2,690 9 View
Dear Colleagues Where can one find the following formula (see the picture attached) for computing a special tridiagonal determinant? Please give a reference in which one can find, or from which...
22 May 2016 9,027 45 View
Dear all What and where is the formula for higher derivatives of a product of many functions? In other words, how to compute higher derivatives of a product of $n$ functions? Concretely speaking,...
13 May 2016 1,459 6 View
How to compute the limit of a complex function below? Thanks. For $b>a>0$, $x\in(-\infty,-a)$, $r>0$, $s\in\mathbb{R}$, and $i=\sqrt{-1}\,$,...
09 April 2016 9,614 5 View
How to define and compute the power-exponential function of a complex variable? For example, how to define and compute the complex function $(\ln z)^{\sin z}$? where $z=x+iy$ is a complex...
07 April 2016 7,205 7 View
What is the name of this continued fraction? How can I express it? How can I compute it? Could you please recommend me some related references? Thank a lot in advance.
07 January 2016 1,004 4 View
Just now I derived a formula for computing the Bernoulli polynomials Bn(t), see the picture attached with this question. But I am not sure whether it is a new one. Have you ever seen a formula...
25 October 2015 999 5 View
What are the special values for the Bell polynomials of the second kind $B_{n,k}(1,1,3!!,5!!,7!!,\dotsc,(2(n-k)-1)!!)$? See the picture below. Please help me find a reference to cite. Thank a lot.
17 June 2015 1,581 8 View
In other words, in which book or article and on which page can I find the following conclusion in the picture? Thank you in advance!
15 January 2015 9,228 5 View
Bell polynomials of the second kind Bn,k(x1,x2,...,xn-k+1) are also called the partial Bell polynomials, where n and k are positive integers. It is known that Bn,k(1,1,...,1) equals Stirling...
28 August 2014 1,670 14 View
It is well known that the secant $\sec z$ may be expanded at $z=0$ into the power series\begin{equation}\label{secant-Series}\sec...
19 July 2014 6,262 34 View
Dear Colleagues I need an inequality for the ratio of two Bernoulli numbers, see attached picture. Could you please help me to find it? Thank you very much. Best regards Feng Qi (F. Qi)
17 July 2014 9,408 20 View
I am asking for a combinatorial interpretation of a formula for Bell numbers in terms of Kummer confluent hypergeometric functions and Stirling numbers of the second kind. See the formula (8) and...
07 April 2014 6,260 1 View
Where to find the answer?
15 October 2013 881 4 View
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15 October 2013 6,860 25 View
