• Title/Summary/Keyword: Mathematics Interesting

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FOURIER SERIES ACCELERATION AND HARDY-LITTLEWOOD SERIES

  • Ciszewski, Regina;Gregory, Jason;Moore, Charles N.;West, Jasmine
    • Journal of applied mathematics & informatics
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    • v.31 no.1_2
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    • pp.263-276
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    • 2013
  • We discuss the effects of the ${\delta}^2$ and Lubkin acceleration methods on the partial sums of Fourier Series. We construct continuous, even H$\ddot{o}$lder continuous functions, for which these acceleration methods fail to give convergence. The constructed functions include some interesting trigonometric series whose properties were investigated by Hardy and Littlewood.

FURTHER EXTENSION OF TWO RESULTS INVOLVING 0F1 DUE TO BAILEY

  • Groth, Frederick;Choi, Junesang;J, Prathima;Rathie, Arjun Kumar
    • East Asian mathematical journal
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    • v.34 no.5
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    • pp.597-600
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    • 2018
  • Bailey presented two Bailey presented two interesting identities involving $_0F_1$, which have been generalized by Choi and Rathie who used two hypergeometric summation formulas due to Qureshi et al. In this note, we aim to show how one can establish, in an elementary way, two generalized formulas involving $_0F_1$ which include the above-mentioned identities as special cases. interesting identities involving 0F1, which

A NEW CLASS OF INTEGRALS INVOLVING HYPERGEOMETRIC FUNCTION

  • Arjun K. Rathie;Choi, June-Sang;Vishakha Nagar
    • Communications of the Korean Mathematical Society
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    • v.15 no.1
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    • pp.51-57
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    • 2000
  • The aim of this research is to provide twenty five integrals involving hypergeometric function in the form of a single integral. Fifty two interesting integrals follow as special cases of our main findings. These results are obtained with the help of generalized Watson's theorem on the sum of a $_3$F$_2$ recently obtained by Lavoie, Grondin and Rathie. The integrals given in this paper are simple, interesting and easily established, and they may be useful.

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Extension of Generalized Hurwitz-Lerch Zeta Function and Associated Properties

  • Choi, Junesang;Parmar, Rakesh Kumar;Raina, Ravinder Krishna
    • Kyungpook Mathematical Journal
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    • v.57 no.3
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    • pp.393-400
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    • 2017
  • Very recently, Srivastava et al. [8] introduced an extension of the Pochhammer symbol and used it to define a generalization of the generalized hypergeometric functions. In this paper, by using the generalized Pochhammer symbol, we extend the generalized Hurwitz-Lerch Zeta function by Goyal and Laddha [6] and investigate some interesting properties which include various integral representations, Mellin transforms, differential formula and generating function. Some interesting special cases of our main results are also considered.

FINITE INTEGRALS ASSOCIATED WITH THE PRODUCT OF ORTHOGONAL POLYNOMIALS AND WRIGHT FUNCTION

  • Khan, Nabiullah;Khan, Mohammad Iqbal;Khan, Owais
    • Honam Mathematical Journal
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    • v.43 no.4
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    • pp.597-612
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    • 2021
  • Several useful and interesting extensions of the various special functions have been introduced by many authors during the last few decades. Various integral formulas associated with Wright function have been studied and a noteworthy amount of work have found in literature. The principal object of the present paper is to evaluate finite integral formulas containing the product of orthogonal polynomials with generalized Wright function. These integral formulas are expressed in terms of Srivastava and Daoust function. Some interesting particular cases are obtained from the main results by specialising the suitable values of the parameters involved.

A Study on the Practice of Performance Assessment in the Elementary School Mathematics - Focussing on Self-assessment and Peer-observation - (초등학교 수학과 수행평가 실천에 관한 연구 - 자기평가.동료평가.관찰평가를 중심으로 -)

  • Kim Song-Ja;Choi Chang-Woo
    • Journal of Elementary Mathematics Education in Korea
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    • v.10 no.1
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    • pp.67-87
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    • 2006
  • This study is to recognize a problem in the practice of performance assessment in elementary school, and to find out some suggestive points for improvement of teaching·learning method in elementary mathematics through assessment by reducing time restriction according to assessment through the practice of self-assessment, peer-assessment and observation, and then by reflecting the results of assessment on teaching learning plan. For that, the questions of study set up are as follows ; 1. How should self-assessment and peer-assessment be applied to in elementary mathematics assessment? 2. How should the time for 'let's play an interesting game' be managed for assessment of elementary mathematics? 3. How should the results of assessment be reflected on the Process of teaching and learning of mathematics? To solve these problems, a researcher of this thesis performed self-assessment, peer-assessment on 40 students of second grade under her charge as a class teacher, and applied observation in the time management process for 'let's play an interesting game' for a semester. self-assessment was made by mathematics journal, self-assessment chart, peer-assessment was by the analysis of conversation record among students in the situations of assessment, and observation was by observation of activity when playing with the results data of play analyzed. the concrete methods of application as follows ; First, mathematics journal was applied $1{\sim}2$ times by each unit with reconstruction into the level of second grade on the basis of the preceding-study models. Second, peer-assessment was applied to the unit-assessment time and the play-activities time by the method of recording·analyzing the contents of conversation among students in the process of assessment. Third, mathematical attitude & dispositions of students making use of the self- assessment table were examined referring to the teaching learning plan. Fourth, the time management for 'let's play an interesting game' was made through the prior recognition of play method and the joyful play-activities by use of the play-plate. Assessment depended on analysis of play-activities results of students making use of an observation form. Fifth, the results of self-assessment, peer-assessment, and observation were analyzed, and then they were made use of as self-observation data, of teacher her/his self, or teaching·learning improvement data. Students' self-assessment datum (mathematics diary, self-assessment sheets, conversation contents in the process of assessment) and observation materials (check lists, Play-activity result materials, conversation contents in the process of play) obtained in the process of application was analyzed as follows ; 1. From the practice of self-assessment in form of mathematics journal, I could obtain not only datum showing how much students was understanding the learning aims by unit time and to any degree they reached but also information about their response to learning datum and favorable type of learning. 2. Assessment by self-assessment chart was useful in planning the mathematics teaching learning process because it helps ascertain mathematical attitude & dispositions of students. 3. Through the application of peer-assessment, students had the opportunity of communicating with other students looking back on his/her explaining process, and teachers could obtain basic materials for assessment of students. 4, In case of time management for 'let's play an interesting game', there was natural extension of play made through time-security by prior looking into the method of play-activity, and then, for a remained time, by making children play a new game. 5, I could easily record the activities of students by use of the observation. form, and make use of it as basic data for descriptive assessment. 6, Each kinds of data obtained from the results of assessment was helpful for securing self-observation materials in the process of teaching learning and for their betterment in mathematics subject. However, because they were in the second grade of elementary school and there was an individual difference, some students could not make use of mathematics diary or self-assessment form properly. In case of these students, assessment data would be obtained through interview or observation. And for effective operation of play, its purpose & method and matters that demand special attention when play-acting should be clearly guided. Also, when applying an effective play in addition to play activities in textbook, to lessons, interesting mathematics lessons could be guided.

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EXTENDED JACOBIN ELLIPTIC FUNCTION METHOD AND ITS APPLICATIONS

  • Chen, Huaitang;Zhang, Hongqing
    • Journal of applied mathematics & informatics
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    • v.10 no.1_2
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    • pp.119-130
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    • 2002
  • An extended Jacobin elliptic function method is presented for constructing exact travelling wave solutions of nonlinear partial differential equations(PDEs) in a unified way. The main idea of this method is to take full advantage of the elliptic equation that Jacobin elliptic functions satisfy and use its solutions to replace Jacobin elliptic functions in Jacobin elliptic function method. It is interesting that many other methods are special cases of our method. Some illustrative equations are investigated by this means.

CAYLEY INTUITIONISTIC FUZZY GRAPHS

  • Akram, Muhammad;Karunambigai, M.G.;Kalaivani, O.K.
    • Journal of applied mathematics & informatics
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    • v.32 no.5_6
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    • pp.827-842
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    • 2014
  • In this paper, we introduce the notion of Cayley intuitionistic fuzzy graphs and investigate some of their properties. We present some interesting properties of intuitionistic fuzzy graphs in terms of algebraic structures. We discuss connectedness in Cayley intuitionistic fuzzy graphs. We also describe different types of ${\alpha}$-connectedness in Cayley intuitionistic fuzzy graphs.

A NOTE ON THE q-EULER NUMBERS AND POLYNOMIALS WITH WEAK WEIGHT α AND q-BERNSTEIN POLYNOMIALS

  • Lee, H.Y.;Jung, N.S.;Kang, J.Y.
    • Journal of applied mathematics & informatics
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    • v.31 no.3_4
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    • pp.523-531
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    • 2013
  • In this paper we construct a new type of $q$-Bernstein polynomials related to $q$-Euler numbers and polynomials with weak weight ${\alpha}$ ; $E^{(\alpha)}_{n,q}$, $E^{(\alpha)}_{n,q}(x)$ respectively. Some interesting results and relationships are obtained.

SOME INTEGRALS ASSOCIATED WITH MULTIINDEX MITTAG-LEFFLER FUNCTIONS

  • KHAN, N.U.;USMAN, T.;GHAYASUDDIN, M.
    • Journal of applied mathematics & informatics
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    • v.34 no.3_4
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    • pp.249-255
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    • 2016
  • The object of the present paper is to establish two interesting unified integral formulas involving Multiple (multiindex) Mittag-Leffler functions, which is expressed in terms of Wright hypergeometric function. Some deduction from these results are also considered.