Theorems on Transform for Product of Generalized  M-Series, I-Function of Two Variables and  It’s Applications

In the present paper we establish four theorem which involves I-function of two variables and generalized M-series. In next section we obtain certain new integrals by application of our theorems by giving suitable values to the parameters. Then main theorem reduces to H-function of two variables etc.

Convolution Integral Equation Involving Generalized Hypergeometric Function and H-function of Two Variables

Journal of Computer and Mathematical Sciences ◽

10.29055/jcms/1080 ◽

2019 ◽

Vol 10 (4) ◽

pp. 954-960

Author(s):

Poonam Kumari ◽

Yashwant Singh

Keyword(s):

Integral Equation ◽

Hypergeometric Function ◽

Generalized Hypergeometric Function ◽

Convolution Integral ◽

Convolution Integral Equation ◽

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

Chronos Journal ◽

10.31618/2658-7556-2019-38-11-1 ◽

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 ◽

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

Cybernetics and Systems Analysis ◽

10.1007/s10559-021-00377-3 ◽

2021 ◽

Author(s):

I. V. Sergienko ◽

O. M. Lytvyn ◽

O. O. Lytvyn ◽

O. V. Tkachenko ◽

A. A. Biloborodov

Keyword(s):

Optimization Of Parameters ◽

Proceedings of the Royal Society of London. Series A, Containing Papers of a Mathematical and Physical Character ◽

The double Fourier series of a discontinuous function

10.1098/rspa.1924.0071 ◽

1924 ◽

Vol 106 (737) ◽

pp. 299-314 ◽

Cited By ~ 1

Keyword(s):

Fourier Series ◽

Finite Number ◽

Double Fourier Series ◽

General Term ◽

Discontinuous Function ◽

Lebesgue Integral ◽

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 .

On the Generalized Weighted Integral Inequality for Double Integrals

Annals of the Alexandru Ioan Cuza University - Mathematics ◽

10.2478/aicu-2014-0008 ◽

2015 ◽

Vol 61 (1) ◽

pp. 169-179 ◽

Cited By ~ 1

Author(s):

Mehmet Zeki Sarikaya

Keyword(s):

Integral Inequality ◽

Independent Variables ◽

Elementary Analysis ◽

Weighted Integral ◽

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.

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

IOSR Journal of Mathematics ◽

10.9790/5728-10445562 ◽

2014 ◽

Vol 10 (4) ◽

pp. 55-62

Author(s):

Yashwant Singh ◽

◽

Harmendra Kumar Mandia

Keyword(s):

Double Integrals

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

International Journal for Research in Applied Sciences and Biotechnology ◽

10.31033/ijrasb.8.4.13 ◽

2021 ◽

Vol 8 (4) ◽

Author(s):

Frédéric Ayant ◽

Prvindra Kumar

Keyword(s):

Functions Of Two Variables ◽

Infinite Integral ◽

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.

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

Computer Physics Communications ◽

10.1016/0010-4655(93)90156-7 ◽

1993 ◽

Vol 78 (1-2) ◽

pp. 211-217 ◽

Cited By ~ 2

Author(s):

M. Nieto-Vesperinas ◽

F.J. Fuentes ◽

R. Navarro ◽

M.J. Perez-Ilzarbe

Keyword(s):

Note on the Hurwitz–Lerch Zeta Function of Two Variables

Symmetry ◽

10.3390/sym12091431 ◽

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 ◽

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.

On Extended General Mittag–Leffler Functions and Certain Inequalities

Fractal and Fractional ◽

10.3390/fractalfract3020032 ◽

2019 ◽

Vol 3 (2) ◽

pp. 32

Author(s):

Marcela V. Mihai ◽

Muhammad Uzair Awan ◽

Muhammad Aslam Noor ◽

Tingsong Du ◽

Artion Kashuri ◽

...

Keyword(s):

Convex Functions ◽

Fractional Integral ◽

Integral Operators ◽

Fractional Integral Operators ◽

Generalized Fractional Integral ◽

Generalized Fractional Integral Operators

In this paper, we introduce and investigate generalized fractional integral operators containing the new generalized Mittag–Leffler function of two variables. We establish several new refinements of Hermite–Hadamard-like inequalities via co-ordinated convex functions.