Hypergeometric functions

Tumor stroma interaction is known to take a crucial role in cancer growth and progression. In the present study, it was performed gene expression analysis of stroma samples with ovarian and breast cancer through an integrative analysis framework to identify common critical biomolecules at multiomics levels. Gene expression datasets were statistically analyzed to identify common differentially expressed genes (DEGs) by comparing tumor stroma and normal stroma samples.

11p thiencuuchu 27-11-2021 9 1   Download

In this paper, we obtain some decomposition formulas for Gaussian triple hypergeometric functions by using certain inverse pairs of symbolic operators introduced by Choi and Hasanov in 2011. Certain transformation formulas for these triple functions have also been obtained.

8p nguaconbaynhay11 07-04-2021 12 2   Download

(BQ) The first edition of this text was published in 1981. Each subsequent revision since then has undergone more than a few changes. Topics have been added, computer software and simulations introduced, and examples redone. What has not changed over the years is our pedagogical focus. As the title indicates, this book is an introduction to mathematical statistics and its applications. Those last three words are not an afterthought.

395p nanhankhuoctai5 01-06-2020 19 2   Download

Formulae expressing explicitly the q-difference derivatives and the moments of the polynomials Pn(x ; q) ∈ T (T ={Pn(x ; q) ∈ Askey–Wilson polynomials: Al-Salam-Carlitz I, Discrete q-Hermite I, Little (Big) q-Laguerre, Little (Big) q-Jacobi, q-Hahn, Alternative q-Charlier) of any degree and for any order in terms of Pi(x ; q) themselves are proved. We will also provide two other interesting formulae to expand the coefficients of general-order q-difference derivatives Dp q f (x), and for the moments xDp q f (x), of an arbitrary function f(x) in terms of its original expansion coefficients.

15p kethamoi1 20-11-2019 14 0   Download

The main objective of this paper is to establish the extension of an extended fractional derivative operator by using an extended beta function recently defined by Parmar et al. by considering the Bessel functions in its kernel.

12p nutifooddau 21-01-2019 16 1   Download

In the present paper, we introduce a new sequence of linear positive operators with the help of generating functions. We obtain some Korovkin type approximation properties for these operators and compute rates of convergence by means of the first and second order modulus of continuities and Peetre’s K-functional.

13p danhdanh27 07-01-2019 26 1   Download

By means of the hypergeometric series approach, we present a new proof of Sun’s conjecture on trigonometric series, which is simpler than the original one due to Sun and Meng. Several further infinite series identities are shown as examples.

7p danhdanh27 08-01-2019 26 2   Download

part 2 book “handbook of mathematical functions with formulas, graphs, and mathematical tables” has contents: coulomb wave functions, hypergeometric functions, weierstrass elliptic and related functions, elliptic integrals, mathieu functions, parabolic cylinder functions, combinatorial analysis,…. and other contents.

276p tieu_vu13 06-08-2018 60 1   Download

To help you major in English with additional material in the process of learning and working, you are invited to consult the book "The Binomial Probability Distribution" below. Hopefully, the books contents useful service for you.

25p bigg421996 03-12-2015 40 2   Download

"A=B" is about identities in general, and hypergeometric identities in particular, with emphasis on computer methods of discovery and proof. The book describes a number of algorithms for doing these tasks, and we intend to maintain the latest versions of the programs that carry out these algorithms on this page. So be sure to consult this page from time to time, and help yourself to the latest versions of the programs.

217p anhnangmuahe2013 05-03-2013 60 8   Download

Tuyển tập báo cáo các nghiên cứu khoa học quốc tế ngành hóa học dành cho các bạn yêu hóa học tham khảo đề tài: Research Article Univalence of Certain Linear Operators Defined by Hypergeometric Function

12p dauphong16 18-02-2012 37 2   Download

Tuyển tập các báo cáo nghiên cứu về hóa học được đăng trên tạp chí sinh học đề tài : On quotients and differences of hypergeometric functions

17p dauphong3 03-01-2012 47 2   Download