• Title/Summary/Keyword: exponential function

Search Result 317, Processing Time 0.146 seconds

MAJORIZATION PROBLEMS FOR UNIFORMLY STARLIKE FUNCTIONS BASED ON RUSCHEWEYH q-DIFFERENTIAL OPERATOR RELATED WITH EXPONENTIAL FUNCTION

  • Vijaya, K.;Murugusundaramoorthy, G.;Cho, N.E.
    • Nonlinear Functional Analysis and Applications
    • /
    • v.26 no.1
    • /
    • pp.71-81
    • /
    • 2021
  • The main object of this present paper is to study some majorization problems for certain classes of analytic functions defined by means of q-calculus operator associated with exponential function.

ON A GENERALIZED UPPER BOUND FOR THE EXPONENTIAL FUNCTION

  • Kim, Seon-Hong
    • Journal of the Chungcheong Mathematical Society
    • /
    • v.22 no.1
    • /
    • pp.7-10
    • /
    • 2009
  • With the introduction of a new parameter $n{\geq}1$, Kim generalized an upper bound for the exponential function that implies the inequality between the arithmetic and geometric means. By a change of variable, this generalization is equivalent to exp $(\frac{n(x-1)}{n+x-1})\;\leq\;\frac{n-1+x^n}{n}$ for real ${n}\;{\geq}\;1$ and x > 0. In this paper, we show that this inequality is true for real x > 1 - n provided that n is an even integer.

  • PDF

NEWTON'S METHOD FOR EQUATIONS RELATED TO EXPONENTIAL FUNCTION

  • Jeong, Moonja
    • Korean Journal of Mathematics
    • /
    • v.9 no.1
    • /
    • pp.67-73
    • /
    • 2001
  • For some equation related with exponential function, we seek roots and find the properties of the roots. By using the relation of the roots and attractors, we find a region in the basin of attraction of the attractor at infinity for Newton's method for solving given equation.

  • PDF

Implementation of Efficient Exponential Function Approximation Algorithm Using Format Converter Based on Floating Point Operation in FPGA (부동소수점 기반의 포맷 컨버터를 이용한 효율적인 지수 함수 근사화 알고리즘의 FPGA 구현)

  • Kim, Jeong-Seob;Jung, Seul
    • Journal of Institute of Control, Robotics and Systems
    • /
    • v.15 no.11
    • /
    • pp.1137-1143
    • /
    • 2009
  • This paper presents the FPGA implementation of efficient algorithms for approximating exponential function based on floating point format data. The Taylor-Maclaurin expansion as a conventional approximation method becomes inefficient since high order expansion is required for the large number to satisfy the approximation error. A format converter is designed to convert fixed data format to floating data format, and then the real number is separated into two fields, an integer field and an exponent field to separately perform mathematic operations. A new assembly command is designed and added to previously developed command set to refer the math table. To test the proposed algorithm, assembly program has been developed. The program is downloaded into the Altera DSP KIT W/STRATIX II EP2S180N Board. Performances of the proposed method are compared with those of the Taylor-Maclaurin expansion.

Meaning and Realization of the Socratic Method - Application to Teaching-Learning of Complex Natural Exponential Function - (소크라테스 방법의 의의와 실천 - 복소지수함수의 교수.학습에의 적용 -)

  • Kim, Seong-A;Jeong, Moon-Ja
    • The Mathematical Education
    • /
    • v.49 no.4
    • /
    • pp.423-436
    • /
    • 2010
  • In this paper we discuss the Socratic method from the aspects of subject education and examine the meaning of the method in mathematics education that is the most suitable subject for the realization of the Socratic method. In addition, as a realization of the Socratic method, we conducted a teaching-learning experiment of complex natural exponential function with a 2nd year college student. The results of the experiment are analyzed with the intention of improving instruction of the complex analysis that is one of the college mathematics courses.

FINDING THE NATURAL SOLUTION TO f(f(x)) = exp(x)

  • Paulsen, William
    • Korean Journal of Mathematics
    • /
    • v.24 no.1
    • /
    • pp.81-106
    • /
    • 2016
  • In this paper, we study the fractional iterates of the exponential function. This is an unresolved problem, not due to a lack of a known solution, but because there are an innite number of solutions, and there is no agreement as to which solution is "best." We will approach the problem by rst solving Abel's functional equation ${\alpha}(e^x)={\alpha}(x)+1$ by perturbing the exponential function so as to produce a real xed point, allowing a unique holomorphic solution. We then use this solution to nd a solution to the unperturbed problem. However, this solution will depend on the way we rst perturbed the exponential function. Thus, we then strive to remove the dependence of the perturbed function. Finally, we produce a solution that is in a sense more natural than other solutions.

COMPLETE MONOTONICITY OF A DIFFERENCE BETWEEN THE EXPONENTIAL AND TRIGAMMA FUNCTIONS

  • Qi, Feng;Zhang, Xiao-Jing
    • The Pure and Applied Mathematics
    • /
    • v.21 no.2
    • /
    • pp.141-145
    • /
    • 2014
  • In the paper, by directly verifying an inequality which gives a lower bound for the first order modified Bessel function of the first kind, the authors supply a new proof for the complete monotonicity of a difference between the exponential function $e^{1/t}$ and the trigamma function ${\psi}^{\prime}(t)$ on (0, ${\infty}$).

A Study on the Process of Constructing the Instantaneous Rate of Change of Exponential Function y=2x at x=0 Based on Understanding of the Natural Constant e (자연상수 e에 대한 이해를 기반으로 지수함수 y=2x의 x=0에서의 순간변화율 구성에 관한 연구)

  • Lee, Dong Gun;Yang, Seong Hyun;Shin, Jaehong
    • School Mathematics
    • /
    • v.19 no.1
    • /
    • pp.95-116
    • /
    • 2017
  • Through the teaching experiments, we investigated a series of processes for obtaining the differential coefficient at x=0 of the exponential function $y=2^x$ based on the process of constructing the natural constant e and the understanding of it. and all of the students who participated in this study were students who had no experience of calculating the derivative of the exponential function. The purpose of this study was not to generalize the responses of students but to suggest implications for mathematical concept mapping related to calculus by analyzing various responses of students participating in experiments. It is expected that the accumulation of research data derived in this kind of research on the way of understanding and composition of learners will be an important basic data for presenting the learning model related to calculus.