A contour integral representation for Mellin transforms

2017 ◽  
pp. 225-226
Keyword(s):  
Integral Representation ◽  
Contour Integral ◽  
Mellin Transforms

Diffraction by a perfectly conducting wedge in an anisotropic plasma

1965 ◽  
Vol 61 (3) ◽  
pp. 767-776 ◽  
Author(s):  
T. R. Faulkner
Keyword(s):  
Magnetic Field ◽  
Electromagnetic Wave ◽  
Difference Equation ◽  
Integral Representation ◽  
Surface Waves ◽  
Uniform Magnetic Field ◽  
Anisotropic Plasma ◽  
Contour Integral ◽  
Anisotropic Dielectric

SummaryThe problem considered is the diffraction of an electromagnetic wave by a perfectly conducting wedge embedded in a plasma on which a uniform magnetic field is impressed. The plasma is assumed to behave as an anisotropic dielectric and the problem is reduced, by employing a contour integral representation for the solution, to solving a difference equation. Surface waves are found to be excited on the wedge and expressions are given for their amplitudes.

scholarly journals Some Difference Equations for Srivastava’s λ-Generalized Hurwitz–Lerch Zeta Functions with Applications

Symmetry ◽  
2019 ◽  
Vol 11 (3) ◽  
pp. 311 ◽  
Author(s):  
Asifa Tassaddiq
Keyword(s):  
Integral Representation ◽  
Difference Equations ◽  
Zeta Functions ◽  
Numerical Computations ◽  
Direct Evaluation ◽  
Mellin Transforms ◽  
The Family

In this article, we establish some new difference equations for the family of λ-generalized Hurwitz–Lerch zeta functions. These difference equations proved worthwhile to study these newly defined functions in terms of simpler functions. Several authors investigated such functions and their analytic properties, but no work has been reported for an estimation of their values. We perform some numerical computations to evaluate these functions for different values of the involved parameters. It is shown that the direct evaluation of involved integrals is not possible for the large values of parameter s; nevertheless, using our new difference equations, we can evaluate these functions for the large values of s. It is worth mentioning that for the small values of this parameter, our results are 100% accurate with the directly computed results using their integral representation. Difference equations so obtained are also useful for the computation of some new integrals of products of λ-generalized Hurwitz–Lerch zeta functions and verified to be consistent with the existing results. A derivative property of Mellin transforms proved fundamental to present this investigation.

THE EIGENVECTORS OF q-DEFORMED CREATION OPERATOR $a_q^+$ AND THEIR PROPERTIES

1995 ◽  
Vol 10 (08) ◽  
pp. 669-675
Author(s):  
GUOXIN JU ◽  
JINHE TAO ◽  
ZIXIN LIU ◽  
MIAN WANG
Keyword(s):  
Integral Representation ◽  
Creation Operator ◽  
Contour Integral ◽  
Root Of Unity

The eigenvectors of q-deformed creation operator [Formula: see text] are discussed for q being real or a root of unity by using the contour integral representation of δ function. The properties for the eigenvectors are also discussed. In the case of qp = 1, the eigenvectors may be normalizable.

Contour integral representation of the on-shell T matrix

1988 ◽  
Vol 66 (9) ◽  
pp. 791-795
Author(s):  
Helmut Kröger
Keyword(s):  
Numerical Calculation ◽  
Integral Representation ◽  
Short Range ◽  
Reference Value ◽  
Potential Scattering ◽  
Contour Integral ◽  
Body System ◽  
T Matrix ◽  
Body Potential ◽  
Separable Interaction

We suggest a contour integral representation for the on-shell T matrix in nonrelativistic N-body potential scattering with strong short range interactions. Results of a numerical calculation in the two-body system using a short range separable interaction of the Yamaguchi type are presented and show fast convergence towards the reference value.

scholarly journals The error bounds of Gauss-Lobatto quadratures for weights of Bernstein-Szegö type

2019 ◽  
Vol 13 (3) ◽  
pp. 733-745
Author(s):  
Rada Mutavdzic ◽  
Aleksandar Pejcev ◽  
Miodrag Spalevic
Keyword(s):  
Integral Representation ◽  
Error Bounds ◽  
Remainder Term ◽  
Contour Integral ◽  
Quadrature Formulas

In this paper, we consider the Gauss-Lobatto quadrature formulas for the Bernstein-Szeg? weights, i.e., any of the four Chebyshev weights divided by a polynomial of the form ?(t) = 1-4?/(1+?)2 t2, where t ?(-1,1) and ? ? (-1,0]. Our objective is to study the kernel in the contour integral representation of the remainder term and to locate the points on elliptic contours where the modulus of the kernel is maximal. We use this to derive the error bounds for mentioned quadrature formulas.

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