THERMAL SCIENCE

International Scientific Journal

Xiao-Jun YangORCID

,

Tasawar HayatORCID

AN ODD ENTIRE-FUNCTION SOLUTION FOR ONE-DIMENSIONAL DIFFUSION EQUATION IN THEORY OF MODULAR FORM

ABSTRACT
This article addresses a new odd entire function of order one structured by the Fourier sine integral, which is the solution of the one-dimensional diffusion equation in theory of modular form.
KEYWORDS
diffusion equation, odd entire function, Fourier sine integral, modular form
PAPER SUBMITTED: 2022-11-05
PAPER REVISED: 2022-11-26
PAPER ACCEPTED: 2022-12-02
PUBLISHED ONLINE: 2023-01-21
DOI REFERENCE: https://doi.org/10.2298/TSCI221105004Y
CITATION EXPORT: view in browser or download as text file
THERMAL SCIENCE YEAR 2023, VOLUME 27, ISSUE No. 1, PAGES [465 - 468]
REFERENCES
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[3] Mordell, L. J., On Mr Ramanujan's Empirical Expansions of Modular Functions, Proceedings of the Cambridge Philosophical Society, 19 (1917), June, pp. 117-124
[4] Rankin, R. A., Contributions to the Theory of Ramanujan's Function τ(n) and Similar Arithmetical Func­tions, Mathematical Proceedings of the Cambridge Philosophical Society, 35 (1939), 03, pp. 351-356, 10.1017/s0305004100021095
[5] Yang, X. J., On the Riemann-Hardy Hypothesis for the Ramanujan Zeta Function, On-line first, 10.48550/arXiv.1811.02418
[6] Cannon-, J. R., et al., A Galerkin Procedure for the Diffusion Equation Subject to the Specification of Mass, SIAM Journal on Numerical Analysis, 24 (1987), 3, pp. 499-515, 10.1137/0724036
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An odd entire-function solution for one-dimensional diffusion equation in theory of modular form

© 2026 Society of Thermal Engineers of Serbia. Published by the Vinča Institute of Nuclear Sciences, National Institute of the Republic of Serbia, Belgrade, Serbia. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution-NonCommercial-NoDerivs 4.0 International licence