Majorization Formulas for a Biharmonic Function of Two Variables

1980 ◽  
Vol 17 (2) ◽  
pp. 207-220
Author(s):  
J. Barkley Rosser
Keyword(s):  
Biharmonic Function ◽  
Function Of Two Variables

MIXED FRACTIONAL DIFFERENTIATION OPERATORS IN HÖLDER SPACES DEFINED BY USUAL HÖLDER CONDITION

2019 ◽  
Author(s):  
T. Mamatov ◽  
R. Sabirova ◽  
D. Barakaev
Keyword(s):  
Fractional Derivative ◽  
Fractional Differentiation ◽  
Hölder Condition ◽  
Hölder Spaces ◽  
Main Interest ◽  
Hölder Class ◽  
Holder Class ◽  
Function Of Two Variables ◽  
Holder Spaces

We study mixed fractional derivative in Marchaud form of function of two variables in Hölder spaces of different orders in each variables. The main interest being in the evaluation of the latter for the mixed fractional derivative in the cases Hölder class defined by usual Hölder condition

Optimization of Parameters in the Generalized D’alembert Formula for a Function of Two Variables

2021 ◽  
Author(s):  
I. V. Sergienko ◽  
O. M. Lytvyn ◽  
O. O. Lytvyn ◽  
O. V. Tkachenko ◽  
A. A. Biloborodov
Keyword(s):  
Optimization Of Parameters ◽  
Function Of Two Variables

scholarly journals The double Fourier series of a discontinuous function

1924 ◽  
Vol 106 (737) ◽  
pp. 299-314 ◽  
Keyword(s):  
Fourier Series ◽  
Finite Number ◽  
Double Fourier Series ◽  
General Term ◽  
Discontinuous Function ◽  
Lebesgue Integral ◽  
Function Of Two Variables

A function of two variables may be expanded in a double Fourier series, as a function of one variable is expanded in an ordinary Fourier series. Purpose that the function f ( x, y ) possesses a double Lebesgue integral over the square (– π < π ; – π < y < π ). Then the general term of the double Fourier series of this function is given by cos = є mn { a mn cos mx cos ny + b mn sin mx sin ny + c mn cos mx sin ny + d mn sin mx cos ny } There є 00 = ¼, є m0 = ½ ( m > 0), є 0n = ½ ( n > 0), є ms = 1 ( m > 0, n >0). the coefficients are given by the formulæ a mn = 1/ π 2 ∫ π -π ∫ π -π f ( x, y ) cos mx cos ny dx dy , obtained by term-by-term integration, as in an ordinary Fourier series. Ti sum of a finite number of terms of the series may also be found as in the ordinary theory. Thus ∫ ms = Σ m μ = 0 Σ n v = 0 A μ v = 1/π 2 ∫ π -π ∫ π -π f (s, t) sin( m +½) ( s - x ) sin ( n + ½) ( t - y )/2 sin ½ ( s - x ) 2 sin ½ ( t - y ) if f ( s , t ) is defined outside the original square by double periodicity, we have sub S ms = 1/π 2 ∫ π 0 ∫ π 0 f ( x + s , y + t ) + f ( x + s , y - t ) + f ( x - s , y + t ) + f ( x - s , y - t ) sin ( m + ½) s / 2 sin ½ s sin ( n + ½) t / 2 sin ½ t ds dt .

scholarly journals On the Generalized Weighted Integral Inequality for Double Integrals

2015 ◽  
Vol 61 (1) ◽  
pp. 169-179 ◽  
Author(s):  
Mehmet Zeki Sarikaya
Keyword(s):  
Integral Inequality ◽  
Independent Variables ◽  
Elementary Analysis ◽  
Weighted Integral ◽  
Function Of Two Variables ◽  
Two Independent Variables ◽  
Double Integrals

Abstract In this paper, we obtain weighted Montgomery’s identities for function of two variables and apply them to give new generalization weighted integral inequality for double integrals involving functions of two independent variables by using fairly elementary analysis.

scholarly journals On Some Double Integrals Involving H -Function of Two Variables and Spheroidal Functions

2014 ◽  
Vol 10 (4) ◽  
pp. 55-62
Author(s):  
Yashwant Singh ◽  
◽  
Harmendra Kumar Mandia
Keyword(s):  
Function Of Two Variables ◽  
Double Integrals

scholarly journals Infinite Integral Involving the Generalized Modified I-Function of Two Variables

2021 ◽  
Vol 8 (4) ◽  
Author(s):  
Frédéric Ayant ◽  
Prvindra Kumar
Keyword(s):  
Functions Of Two Variables ◽  
Infinite Integral ◽  
Function Of Two Variables

In the present paper, we evaluate the general infinite integral involving the generalized modified I-functions of two variables. At the end, we shall see several corollaries and remarks.

scholarly journals A FORTRAN routine to estimate a function of two variables from its autocorrelation

1993 ◽  
Vol 78 (1-2) ◽  
pp. 211-217 ◽  
Author(s):  
M. Nieto-Vesperinas ◽  
F.J. Fuentes ◽  
R. Navarro ◽  
M.J. Perez-Ilzarbe
Keyword(s):  
Function Of Two Variables

scholarly journals Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽  
2020 ◽  
Vol 12 (9) ◽  
pp. 1431
Author(s):  
Junesang Choi ◽  
Recep Şahin ◽  
Oğuz Yağcı ◽  
Dojin Kim
Keyword(s):  
Zeta Function ◽  
Generating Functions ◽  
Recurrence Relations ◽  
Zeta Functions ◽  
Integral Representations ◽  
Lerch Zeta Function ◽  
Derivative Formulas ◽  
The One ◽  
Function Of Two Variables

A number of generalized Hurwitz–Lerch zeta functions have been presented and investigated. In this study, by choosing a known extended Hurwitz–Lerch zeta function of two variables, which has been very recently presented, in a systematic way, we propose to establish certain formulas and representations for this extended Hurwitz–Lerch zeta function such as integral representations, generating functions, derivative formulas and recurrence relations. We also point out that the results presented here can be reduced to yield corresponding results for several less generalized Hurwitz–Lerch zeta functions than the extended Hurwitz–Lerch zeta function considered here. For further investigation, among possibly various more generalized Hurwitz–Lerch zeta functions than the one considered here, two more generalized settings are provided.

Sign in / Sign up

Export Citation Format

Share Document