Pre-functions and Extended pre-functions of Complex Variables

Thirumalai A; Muthunagai K; Ritu Agarwal

doi:10.46481/jnsps.2023.1427

Authors

Thirumalai A School of Advanced Sciences, VIT University, Chennai-600 127, Tamil Nadu, India
Muthunagai K
muthunagai@vit.ac.in
School of Advanced Sciences, VIT University, Chennai-600 127, Tamil Nadu, India
Ritu Agarwal Department of Mathematics, Malaviya National Institute of Technology, Jaipur-302017, India

Keywords:

pre-exponential functions, pre-trigonometric functions, pre-hyperbolic functions, Extended pre-functions.

Abstract

Pre-functions are functions that possess a sequence $\{f_{n}(z,\beta)\}$ which tends to one of the elementary functions as $n$ tends to infinity and $\beta$ tends to 0. The main objective of this paper is to broaden the scope of pre-functions from functions of a real variable to functions of a complex variable by introducing pre-functions of a complex variable. We have analyzed the pre-functions of a complex variable for their properties. The pre-Laguerre, pre-Bessel and pre-Legendre polynomials of a complex variable have been obtained as special cases. Graphs have been used to visualize complex pre-functions.

Dimensions

REFERENCES

S. G. Deo & G. W. Howell,”A highway to trigonometry”, Bull. Marathawada Mathematical Society 1 (2000) 26.

R.B. Khandeparkar, S. Deo & D. B. Dhaigude, ”pre-exponential and pre-trigonometric Functions”, Communications in Applied Analysis 14 (2010) 99.

V. O. Atabo & S. O. Adee, ” A new special 15-step block method for solving general fourth-order ordinary differential equations”, Journal of the Nigerian Society of Physical Sciences 3 (2021) 308. https://doi.org/10.46481/jnsps.2021.337 DOI: https://doi.org/10.46481/jnsps.2021.337

S. G. Deo, V. Raghavendra, R. Kar & V.Lakshmikantham, ”ordinary differential equations”, McGraw-Hill Education, 1997.

O. O. Enoch, A. A. Adejimi A. & Lukman O. Salaudeen,”The Derivation of the Riemann Analytic Continuation Formula from the Euler’s Quadratic Equation”, Journal of the Nigerian Society of Physical Sciences 5 (2023) 967. https://doi.org/10.46481/jnsps.2023.967 DOI: https://doi.org/10.46481/jnsps.2023.967

I.S. Sokolnikoff, ”R.M. Redheffer”, Mathematics of Physics and Modern Engineering New York (1966).

R. B. Khandeparkar, ”Pretrigonometric and prehyperbolic functions via Laplace transforms”, Neural, Parallel and Scientific Computations 18 (2010) 423.

S. B. Dhaigude & D. Chandradeepa, ”Some results on Pre-functions and Differential Equations”, Bull. Marathawada Mathematical Society, 12 (2011) 18.

S. B. Dhaigude & C. D. Dhaigude, ”Prefunctions and Integral Equations via Laplace Transforms”, International Journal of Engineering Sciences, 2 (2013) 204.

M. Mahmoudi & M. V. Kazemi, ”Solving singular BVPs ordinary differential equations by modified homotopy perturbation method”, Journal of mathematics and computer science 7 (2013) 138. DOI: https://doi.org/10.22436/jmcs.07.02.07