• Title/Summary/Keyword: Function of University

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EXTENDED WRIGHT-BESSEL FUNCTION AND ITS PROPERTIES

  • Arshad, Muhammad;Mubeen, Shahid;Nisar, Kottakkaran Sooppy;Rahman, Gauhar
    • Communications of the Korean Mathematical Society
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    • v.33 no.1
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    • pp.143-155
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    • 2018
  • In this present paper, our aim is to introduce an extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ which is established with the help of the extended beta function. Also, we investigate certain integral transforms and generalized integration formulas for the newly defined extended Wright-Bessel function $J^{{\lambda},{\gamma},c}_{{\alpha},q}(z)$ and the obtained results are expressed in terms of Fox-Wright function. Some interesting special cases involving an extended Mittag-Leffler functions are deduced.

CERTAIN INTEGRAL REPRESENTATIONS OF EULER TYPE FOR THE EXTON FUNCTION X5

  • Choi, June-Sang;Hasanov, Anvar;Turaev, Mamasali
    • Honam Mathematical Journal
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    • v.32 no.3
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    • pp.389-397
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    • 2010
  • Exton introduced 20 distinct triple hypergeometric functions whose names are Xi (i = 1,$\ldots$, 20) to investigate their twenty Laplace integral representations whose kernels include the confluent hypergeometric functions $_0F_1$, $_1F_1$, a Humbert function $\Psi_2$, a Humbert function $\Phi_2$. The object of this paper is to present 25 (presumably new) integral representations of Euler types for the Exton hypergeometric function $X_5$ among his twenty $X_i$ (i = 1,$\ldots$, 20), whose kernels include the Exton function X5 itself, the Exton function $X_6$, the Horn's functions $H_3$ and $H_4$, and the hypergeometric function F = $_2F_1$.

CERTAIN NEW EXTENSION OF HURWITZ-LERCH ZETA FUNCTION

  • KHAN, WASEEM A.;GHAYASUDDIN, M.;AHMAD, MOIN
    • Journal of applied mathematics & informatics
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    • v.37 no.1_2
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    • pp.13-21
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    • 2019
  • In the present research paper, we introduce a further extension of Hurwitz-Lerch zeta function by using the generalized extended Beta function defined by Parmar et al.. We investigate its integral representations, Mellin transform, generating functions and differential formula. In view of diverse applications of the Hurwitz-Lerch Zeta functions, the results presented here may be potentially useful in some related research areas.

ON A CERTAIN EXTENSION OF THE RIEMANN-LIOUVILLE FRACTIONAL DERIVATIVE OPERATOR

  • Nisar, Kottakkaran Sooppy;Rahman, Gauhar;Tomovski, Zivorad
    • Communications of the Korean Mathematical Society
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    • v.34 no.2
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    • pp.507-522
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    • 2019
  • The main aim of this present paper is to present a new extension of the fractional derivative operator by using the extension of beta function recently defined by Shadab et al. [19]. Moreover, we establish some results related to the newly defined modified fractional derivative operator such as Mellin transform and relations to extended hypergeometric and Appell's function via generating functions.

EULER SUMS EVALUATABLE FROM INTEGRALS

  • Jung, Myung-Ho;Cho, Young-Joon;Choi, June-Sang
    • Communications of the Korean Mathematical Society
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    • v.19 no.3
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    • pp.545-555
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    • 2004
  • Ever since the time of Euler, the so-called Euler sums have been evaluated in many different ways. We give here a proof of the classical Euler sum by following Lewin's method. We also consider some related formulas involving Euler sums, which are evaluatable from some known definite integrals.

Correlations among the Continence Function, Cognitive Function and Activities of Daily Living in Elderly Male Patients with Dementia in a Geriatric Hospital

  • Kim, Hong Rae;Shin, Hee Joon;Wang, Joong San
    • Journal of International Academy of Physical Therapy Research
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    • v.7 no.1
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    • pp.972-978
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    • 2016
  • The purpose of this study was to identify correlations among the continence function, cognitive function, and activities of daily living(ADL) in elderly male patients with dementia in geriatric hospitals. The subjects were 64 patients aged 65 or above who were diagnosed with dementia among the hospitalized male patients in a geriatric hospital. For the subjects' cognitive function, a questionnaire developed for the Korean Mini Mental Status Examination(K-MMSE) was used. For the continence function and ADL, data were collected using a patient evaluation table. As a result, a lower level of cognitive function resulted in corresponding higher levels of dependence in all items of ADL except bathing(p<.05), and a lower level of cognitive function led to corresponding declines in the continence function(bowel control, bladder control)(p<.01). In addition, a higher level of dependence in ADL resulted in corresponding higher levels of difficulty in bowel and bladder control(p<.01). This study showed correlations among the cognitive function, ADL, and continence function of elderly men with dementia. The results of this study may be used as basic data for the management and treatment of hospitalized elderly male patients with dementia in geriatric hospitals.

GENERATING FUNCTIONS OF (p, q)-ANALOGUE OF ALEPH-FUNCTION SATISFYING TRUESDELL'S ASCENDING AND DESCENDING Fp,q-EQUATION

  • ALTAF A. BHAT;M. YOUNUS BHAT;H. MAQBOOL;D.K. JAIN
    • Journal of applied mathematics & informatics
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    • v.41 no.2
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    • pp.373-386
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    • 2023
  • In this paper we have obtained various forms of (p, q)-analogue of Aleph-Function satisfying Truesdell's ascending and descending Fp,q-equation. These structures have been employed to arrive at certain generating functions for (p, q)-analogue of Aleph-Function. Some specific instances of these outcomes as far as (p, q)-analogue of I-function, H-function and G-functions have likewise been obtained.

CONTINUITY OF THE FRACTIONAL PART FUNCTION AND DYNAMICS OF CIRCLE

  • LAL, BABU;MIGLANI, ASEEM;SINGH, VIZENDER
    • Journal of applied mathematics & informatics
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    • v.40 no.5_6
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    • pp.1167-1179
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    • 2022
  • In this paper, we obtain some subsets of real numbers (ℝ) on which a fractional part function is defined as a real-valued continuous function. This gives rise to the analysis of the continuous properties of the fractional part function as a real-valued function. The analysis of fractional part function is helpful in the study of the dynamics of circle.

GENERALIZATION OF EXTENDED BETA FUNCTION, HYPERGEOMETRIC AND CONFLUENT HYPERGEOMETRIC FUNCTIONS

  • Lee, Dong-Myung;Rathie, Arjun K.;Parmar, Rakesh K.;Kim, Yong-Sup
    • Honam Mathematical Journal
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    • v.33 no.2
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    • pp.187-206
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    • 2011
  • The main object of this paper is to present generalization of extended beta function, extended hypergeometric and confluent hypergeometric function introduced by Chaudhry et al. and obtained various integral representations, properties of beta function, Mellin transform, beta distribution, differentiation formulas transform formulas, recurrence relations, summation formula for these new generalization.