Inverse Laplace Transform of Some Rational Functions
نویسندگان
چکیده
منابع مشابه
On the Inverse Laplace-stieltjes Transform of A-stable Rational Functions
Let r be an A-stable rational approximation of the exponential function of order q ≥ 1 and let t > 0. It is shown that the inverse LaplaceStieltjes transforms αn : s→ αn∗(ns t ) of rn(z) := r n( tz n ) converge in Lp(R+) to the Heaviside function Ht with a rate of t1/pn−1/2p(ln(n+1))1−1/p. Moreover, for 0 ≤ k ≤ q, the k-th antiderivatives of αn converge in Lp(R+) to the k-th antiderivative of t...
متن کاملLaplace transform of certain functions with applications
The Laplace transform of the functions tν(1+ t)β, Reν > −1, is expressed in terms of Whittaker functions. This expression is exploited to evaluate infinite integrals involving products of Bessel functions, powers, exponentials, and Whittaker functions. Some special cases of the result are discussed. It is also demonstrated that the famous identity ∫∞ 0 sin(ax)/xdx =π/2 is a special case of our ...
متن کاملInverse Laplace transform method for multiple solutions of the fractional Sturm-Liouville problems
In this paper, inverse Laplace transform method is applied to analytical solution of the fractional Sturm-Liouville problems. The method introduces a powerful tool for solving the eigenvalues of the fractional Sturm-Liouville problems. The results how that the simplicity and efficiency of this method.
متن کاملApplication of Numerical Inverse Laplace Transform Algorithms in Fractional Calculus
It is known that the Laplace transform is frequently used to solve fractional-order differential equations. Unlike integer-order differential equations, fractional-order differential equations always lead to difficulties in calculating inversion of Laplace transforms. Motivated by finding an easy way to numerically solve the fractional-order differential equations, we investigated the validity ...
متن کاملLaplace Transform
We have seen before that Fourier analysis is very useful in the study of signals and linear and time invariant (LTI) systems. The main reason is that a lot of signals can be expressed as a linear combination of complex exponentials of the form e with s = jw. There are many properties that still apply when s is not restricted to be pure imaginary. That is why we introduce a generalization of the...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Acta Physica Polonica A
سال: 2012
ISSN: 0587-4246,1898-794X
DOI: 10.12693/aphyspola.122.966