On rational classical orthogonal polynomials and their application for explicit computation of inverse Laplace transforms

On Rational Classical Orthogonal Polynomials and Their Application for Explicit Computation of Inverse Laplace Transforms

From the main equation (ax2 + bx + c)y′′ n (x) + (dx + e)y′ n(x)− n((n− 1)a+ d)yn(x) = 0, n∈ Z+, six finite and infinite classes of orthogonal polynomials can be extracted. In this work, first we have a survey on these classes, particularly on finite classes, and their corresponding rational orthogonal polynomials, which are generated by Mobius transform x = pz−1 + q, p = 0, q ∈ R. Some new int...

Fair and Square Computation of Inverse -Transforms of Rational Functions

All methods presented in textbooks for computing inverse -transforms of rational functions have some limitation: 1) the direct division method does not, in general, provide enough information to derive an analytical expression for the time-domain sequence whose -transform is ; 2) computation using the inversion integral method becomes labored when has poles at the origin of the complex plane; 3...

Laplace and Segal-bargmann Transforms on Hermitian Symmetric Spaces and Orthogonal Polynomials

Recurrences and explicit formulae for the expansion and connection coefficients in series of the product of two classical discrete orthogonal polynomials

Suppose that for an arbitrary function $f(x,y)$ of two discrete variables, we have the formal expansions. [f(x,y)=sumlimits_{m,n=0}^{infty }a_{m,n},P_{m}(x)P_{n}(y),] $$‎ ‎x^{m}P_{j}(x)=sumlimits_{n=0}^{2m}a_{m,,n}(j)P_{j+m-n}(x)‎,$$ ‎we find the coefficients $b_{i,j}^{(p,q,ell‎ ,‎,r)}$ in the expansion‎ $$‎ ‎x^{ell }y^{r},nabla _{x}^{p}nabla _{y}^{q},f(x,y)=x^{ell‎ ‎}y^{r}f^{(p,q)}(x,y) =sumli...

application of upfc based on svpwm for power quality improvement

در سالهای اخیر،اختلالات کیفیت توان مهمترین موضوع می باشد که محققان زیادی را برای پیدا کردن راه حلی برای حل آن علاقه مند ساخته است.امروزه کیفیت توان در سیستم قدرت برای مراکز صنعتی،تجاری وکاربردهای بیمارستانی مسئله مهمی می باشد.مشکل ولتاژمثل شرایط افت ولتاژواضافه جریان ناشی از اتصال کوتاه مدار یا وقوع خطا در سیستم بیشتر مورد توجه می باشد. برای مطالعه افت ولتاژ واضافه جریان،محققان زیادی کار کرده ...