A note on two-variable Lommel matrix functions

2018 ◽  
Vol 11 (03) ◽  
pp. 1850041 ◽  
Author(s):  
Ayman Shehata
Keyword(s):  
Matrix Functions ◽  
Functions Of Two Variables ◽  
Special Cases

The aim of the present work is to develop a pair of Lommel matrix functions of two variables suggested by the Bessel matrix functions and some of their properties are studied to be special cases of our results.

On the basic hypergeometric matrix functions of two variables

2017 ◽  
Vol 67 (1) ◽  
pp. 1-19 ◽  
Author(s):  
Ravi Dwivedi ◽  
Vivek Sahai
Keyword(s):  
Matrix Functions ◽  
Functions Of Two Variables

scholarly journals An identity for a class of arithmetical functions of several variables

1993 ◽  
Vol 16 (2) ◽  
pp. 355-358
Author(s):  
Pentti Haukkanen
Keyword(s):  
Wide Class ◽  
Trigonometric Sum ◽  
Arithmetical Functions ◽  
Functions Of Two Variables ◽  
Several Variables ◽  
Special Cases

Johnson [1] evaluated the sum∑d|n|C(d;r)|, whereC(n;r)denotes Ramanujan's trigonometric sum. This evaluation has been generalized to a wide class of arithmetical functions of two variables. In this paper, we generalize this evaluation to a wide class of arithmetical functions of several variables and deduce as special cases the previous evaluations.

scholarly journals On the Extended Hypergeometric Matrix Functions and Their Applications for the Derivatives of the Extended Jacobi Matrix Polynomial

2020 ◽  
Vol 2020 ◽  
pp. 1-8 ◽  
Author(s):  
Fuli He ◽  
Ahmed Bakhet ◽  
M. Abdalla ◽  
M. Hidan
Keyword(s):  
Matrix Function ◽  
Matrix Polynomial ◽  
Jacobi Matrix ◽  
Integral Representations ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Derivatives Of

In this paper, we obtain some generating matrix functions and integral representations for the extended Gauss hypergeometric matrix function EGHMF and their special cases are also given. Furthermore, a specific application for the extended Gauss hypergeometric matrix function which includes Jacobi matrix polynomials is constructed.

On the hypergeometric matrix functions of two variables

2017 ◽  
Vol 66 (9) ◽  
pp. 1819-1837 ◽  
Author(s):  
Ravi Dwivedi ◽  
Vivek Sahai
Keyword(s):  
Matrix Functions ◽  
Functions Of Two Variables

scholarly journals An extension of the generalized Hurwitz-Lerch Zeta function of two variables

Filomat ◽  
2017 ◽  
Vol 31 (1) ◽  
pp. 91-96 ◽  
Author(s):  
Junesang Choi ◽  
Rakesh Parmar
Keyword(s):  
Zeta Function ◽  
Zeta Functions ◽  
Summation Formula ◽  
Integral Representations ◽  
Contour Integral ◽  
Functions Of Two Variables ◽  
Special Cases ◽  
Lerch Zeta Function ◽  
Function Of Two Variables

The main object of this paper is to introduce a new extension of the generalized Hurwitz-Lerch Zeta functions of two variables. We then systematically investigate such its several interesting properties and related formulas as (for example) various integral representations, which provide certain new and known extensions of earlier corresponding results, a summation formula and Mellin-Barnes type contour integral representations. We also consider some important special cases.

scholarly journals Monotone matrix functions of two variables

2001 ◽  
Vol 328 (1-3) ◽  
pp. 131-152 ◽  
Author(s):  
Mandeep Singh ◽  
H.L. Vasudeva
Keyword(s):  
Matrix Functions ◽  
Functions Of Two Variables ◽  
Monotone Matrix

scholarly journals Two Variables Shivley’s Matrix Polynomials

Symmetry ◽  
2019 ◽  
Vol 11 (2) ◽  
pp. 151 ◽  
Author(s):  
Fuli He ◽  
Ahmed Bakhet ◽  
M. Hidan ◽  
M. Abdalla
Keyword(s):  
Recurrence Relations ◽  
Summation Formula ◽  
Matrix Functions ◽  
Matrix Polynomials ◽  
Special Cases ◽  
Generating Matrix Functions ◽  
Generating Matrix ◽  
Matrix Recurrence Relations

The principal object of this paper is to introduce two variable Shivley’s matrix polynomials and derive their special properties. Generating matrix functions, matrix recurrence relations, summation formula and operational representations for these polynomials are deduced. Finally, Some special cases and consequences of our main results are also considered.

scholarly journals An identity for a class of arithmetical functions of two variables

1988 ◽  
Vol 11 (2) ◽  
pp. 351-354
Author(s):  
J. Chidambaraswamy ◽  
P. V. Krishnaiah
Keyword(s):  
Positive Integer ◽  
Wide Class ◽  
Arithmetical Functions ◽  
Functions Of Two Variables ◽  
Special Cases ◽  
Ramanujan’S Sum ◽  
Ramanujan's Sum

For a positive integerr, letr∗denote the quotient ofrby its largest squarefree divisor(1∗=1). Recently, K. R. Johnson proved that(∗)∑d|n|C(d,r)|=r∗∏pa‖nr∗p+r(a+1)∏pa‖nr∗p|r(a(p−1)+1)   or   0according asr∗|nor not whereC(n,r)is the well known Ramanujan's sum. In this paper, using a different method, we generalize(∗)to a wide class of arithmetical functions of2variables and deduce as special cases(∗)and similar formulae for several generalizations of Ramanujan''s sum.

Electron Beam Damage of Biomolecules Assessed by Energy Loss Spectroscopy

1978 ◽  
Vol 36 (3) ◽  
pp. 61-69
Author(s):  
M. Isaacson ◽  
M.L. Collins ◽  
M. Listvan
Keyword(s):  
Electron Microscopy ◽  
Radiation Damage ◽  
Structural Integrity ◽  
Analytical Electron Microscopy ◽  
High Dose ◽  
Dose Rates ◽  
Special Cases ◽  
Analytical Electron ◽  
Atom Migration ◽  
Beam Damage

Over the past five years it has become evident that radiation damage provides the fundamental limit to the study of blomolecular structure by electron microscopy. In some special cases structural determinations at very low doses can be achieved through superposition techniques to study periodic (Unwin & Henderson, 1975) and nonperiodic (Saxton & Frank, 1977) specimens. In addition, protection methods such as glucose embedding (Unwin & Henderson, 1975) and maintenance of specimen hydration at low temperatures (Taylor & Glaeser, 1976) have also shown promise. Despite these successes, the basic nature of radiation damage in the electron microscope is far from clear. In general we cannot predict exactly how different structures will behave during electron Irradiation at high dose rates. Moreover, with the rapid rise of analytical electron microscopy over the last few years, nvicroscopists are becoming concerned with questions of compositional as well as structural integrity. It is important to measure changes in elemental composition arising from atom migration in or loss from the specimen as a result of electron bombardment.

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