Evaluation of Some Improper Integrals Involving Hyperbolic Functions

2007 ◽  
Vol 114 (4) ◽  
pp. 341-343
Author(s):  
Michael A. Allen
Keyword(s):  
Hyperbolic Functions ◽  
Improper Integrals

Mathematical analysis in examples and tasks. Part 1

2020 ◽  
Author(s):  
Galina Zhukova ◽  
Margarita Rushaylo
Keyword(s):  
Mathematical Analysis ◽  
Continuous Functions ◽  
Advanced Mathematics ◽  
Hyperbolic Functions ◽  
Integral Calculus ◽  
Postgraduate Students ◽  
Background Material ◽  
Improper Integrals ◽  
Sets Theory ◽  
Independent Work

The purpose of the textbook is to help students to master basic concepts and research methods used in mathematical analysis. In part 1 of the proposed cycle of workshops on the following topics: theory of sets, theory of limits, theory of continuous functions; differential calculus of functions of one variable, its application to the study of the properties of functions and graph; integral calculus of functions of one variable: indefinite, definite, improper integrals; hyperbolic functions; applications of integral calculus to the analysis and solution of practical problems. For the development of each topic the necessary theoretical and background material, reviewed a large number of examples with detailed analysis and solutions, the options for independent work. For self-training and quality control of the obtained knowledge provides exercises and problems with answers and guidance. For teachers, students and postgraduate students studying advanced mathematics.

The mathematical analysis. Volume 1

2020 ◽  
Author(s):  
Galina Zhukova ◽  
Margarita Rushaylo
Keyword(s):  
Mathematical Analysis ◽  
Differential Calculus ◽  
Real Variable ◽  
Hyperbolic Functions ◽  
Integral Calculus ◽  
Postgraduate Students ◽  
First Semester ◽  
Improper Integrals ◽  
Basic Concepts ◽  
Sets Theory

The aim of the tutorial is to help students to master the basic concepts and methods of the study of calculus. Volume 1 explores the following topics: theory of sets, theory of limits; differential calculus of functions of one variable; investigation of the properties of functions and graphing; integral calculus of functions of one real variable (indefinite, definite and improper integrals), the technique of integration; hyperbolic functions; applications to the analysis and solution of practical problems. These topics are studied in universities, as a rule, in the first semester in the framework of self-discipline "Mathematical analysis" or the course "Higher mathematics", "Mathematics". Great attention is paid to comparison of these methods, the proper choice of study design tasks, analyze complex situations that arise in the study of these branches of mathematical analysis. For teachers, students and postgraduate students studying mathematical analysis.

On the improvement of q-deformed hyperbolic functions

2021 ◽  
Author(s):  
J. Morales ◽  
J. J. Peña ◽  
J. García-Ravelo
Keyword(s):  
Hyperbolic Functions

scholarly journals Application of the Efros Theorem to the Function Represented by the Inverse Laplace Transform of s−μ exp(−sν)

Symmetry ◽  
2021 ◽  
Vol 13 (2) ◽  
pp. 354
Author(s):  
Alexander Apelblat ◽  
Francesco Mainardi
Keyword(s):  
Laplace Transform ◽  
Operational Calculus ◽  
Inverse Laplace Transform ◽  
Elementary Functions ◽  
Hyperbolic Functions ◽  
Error Functions ◽  
Convolution Integrals ◽  
Special Case ◽  
Integral Identities ◽  
Finite Integrals

Using a special case of the Efros theorem which was derived by Wlodarski, and operational calculus, it was possible to derive many infinite integrals, finite integrals and integral identities for the function represented by the inverse Laplace transform. The integral identities are mainly in terms of convolution integrals with the Mittag–Leffler and Volterra functions. The integrands of determined integrals include elementary functions (power, exponential, logarithmic, trigonometric and hyperbolic functions) and the error functions, the Mittag–Leffler functions and the Volterra functions. Some properties of the inverse Laplace transform of s−μexp(−sν) with μ≥0 and 0<ν<1 are presented.

The q-pell hyperbolic functions

2012 ◽  
Author(s):  
A. Güncan ◽  
Ş. Akduman
Keyword(s):  
Hyperbolic Functions

scholarly journals Improving CAS capabilities: New rules for computing improper integrals

2018 ◽  
Vol 316 ◽  
pp. 525-540 ◽  
Author(s):  
José L. Galán-García ◽  
Gabriel Aguilera-Venegas ◽  
María Á. Galán-García ◽  
Pedro Rodríguez-Cielos ◽  
Iván Atencia-Mc.Killop
Keyword(s):  
Improper Integrals
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