اشترك بالحزمة الذهبية واحصل على وصول غير محدود شمرا أكاديميا
تسجيل مستخدم جديدThe asymptotic expansion of the Bateman and Havelock functions of large order and argument
59
0
0.0
(
0
)
تأليف
R B Paris
اسأل ChatGPT حول البحث
ﻻ يوجد ملخص باللغة العربية
Asymptotic expansions for the Bateman and Havelock functions defined respectively by the integrals [frac{2}{pi}int_0^{pi/2} !!!begin{array}{c} cossinend{array}!(xtan u- u u),du] are obtained for large real $x$ and large order $ u>0$ when $ u=O(|x|)$. The expansions are obtained by application of the method of steepest descents combined with an inversion process to determine the coefficients. Numerical results are presented to illustrate the accuracy of the different expansions obtained.
قيم البحث
اقرأ أيضاً
We examine the sum of modified Bessel functions with argument depending quadratically on the summation index given by [S_ u(a)=sum_{ngeq 1} (frac{1}{2} an^2)^{- u} K_ u(an^2)qquad (|arg,a|<pi/2)] as the parameter $|a|to 0$. It is shown that the posit
ive real $a$-axis is a Stokes line, where an infinite number of increasingly subdominant exponentially small terms present in the asymptotic expansion undergo a smooth, but rapid, transition as this ray is crossed. Particular attention is devoted to the details of the expansion on the Stokes line as $ato 0$ through positive values. Numerical results are presented to support the asymptotic theory.
The LULU operators, well known in the nonlinear multiresolution analysis of sequences, are extended to functions defined on a continuous domain, namely, a real interval. We show that the extended operators replicate the essential properties of their
discrete counterparts. More precisely, they form a fully ordered semi-group of four elements, preserve the local trend and the total variation.
In this paper, sums represented in (3) are studied. The expressions are derived in terms of Bessel functions of the first and second kinds and their integrals. Further, we point out the integrals can be written as a Meijer G function.
Asymptotic expansion of the eigenvalues of a Toeplitz matrix with real symbol. This work provides two results obtained as a consequence of an inversion formula for Toeplitz matrices with real symbol. First we obtain an symptotic expression for the mi
nimal eigenvalues of a Toeplitz matrix with a symbol which is periodic, even and derivable on $[0, 2pi[$. Next we prove that a Toeplitz band matrix with a symbol without zeros on the united circle is invertible with an inverse which is essentially a band matrix. As a consequence of this last statement we give an asymptotic estimation for the entries of the inverse of a Toplitz matrix with a regular symbol.
Self-consistent treatment of cosmological structure formation and expansion within the context of classical general relativity may lead to extra expansion above that expected in a structureless universe. We argue that in comparison to an early-epoch,
extrapolated Einstein-de Sitter model, about 10-15% extra expansion is sufficient at the present to render superfluous the dark energy 68% contribution to the energy density budget, and that this is observationally realistic.
سجل دخول لتتمكن من نشر تعليقات
التعليقات
جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
