ترغب بنشر مسار تعليمي؟ اضغط هنا

On the representation of cylinder functions

133   0   0.0 ( 0 )
 نشر من قبل Enrico De Micheli
 تاريخ النشر 2019
  مجال البحث فيزياء
والبحث باللغة English
 تأليف Enrico De Micheli




اسأل ChatGPT حول البحث

In this paper, we present a mixed-type integral-sum representation of the cylinder functions $mathscr{C}_mu(z)$, which holds for unrestricted complex values of the order $mu$ and for any complex value of the variable $z$. Particular cases of these representations and some applications, which include the discussion of limiting forms and representations of related functions, are also discussed.



قيم البحث

اقرأ أيضاً

121 - Enrico De Micheli 2017
A Fourier-type integral representation for Bessels function of the first kind and complex order is obtained by using the Gegenbuaer extension of Poissons integral representation for the Bessel function along with a trigonometric integral representati on of Gegenbauers polynomials. This representation lets us express various functions related to the incomplete gamma function in series of Bessels functions. Neumann series of Bessel functions are also considered and a new closed-form integral representation for this class of series is given. The density function of this representation is simply the analytic function on the unit circle associated with the sequence of coefficients of the Neumann series. Examples of new closed-form integral representations of special functions are also presented.
71 - Masatoshi Noumi 2016
We investigate the structure of $tau$-functions for the elliptic difference Painleve equation of type $E_8$. Introducing the notion of ORG $tau$-functions for the $E_8$ lattice, we construct some particular solutions which are expressed in terms of e lliptic hypergeometric integrals. Also, we discuss how this construction is related to the framework of lattice $tau$-functions associated with the configuration of generic nine points in the projective plane.
177 - Yilin Chen 2021
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.
145 - Ilia Krasikov 2002
We shall give bounds on the spacing of zeros of certain functions belonging to the Laguerre-Polya class and satisfying a second order differential equation. As a corollary we establish new sharp inequalities on the extreme zeros of the Hermite, Lague rre and Jacobi polinomials, which are uniform in all the parameters.
A demonstration of how the point symmetries of the Chazy Equation become nonlocal symmetries for the reduced equation is discussed. Moreover we construct an equivalent third-order differential equation which is related to the Chazy Equation under a g eneralized transformation, and find the point symmetries of the Chazy Equation are generalized symmetries for the new equation. With the use of singularity analysis and a simple coordinate transformation we construct a solution for the Chazy Equation which is given by a Right Painleve Series. The singularity analysis is applied to the new third-order equation and we find that it admits two solutions, one given by a Left Painleve Series and one given by a Right Painleve Series where the leading-order behaviors and the resonances are explicitly those of the Chazy Equation.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا