THERMAL SCIENCE

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Thermal Science - Online First

Authors of this Paper

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Xiao-Jun Yang

,

Tasawar Hayat

online first only

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
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
  5. Yang, X. J., On the Riemann-Hardy hypothesis for the Ramanujan zeta function, doi.org/10.48550/arXiv.1811.02418
  6. Cannon, J. R., Esteva, S. P., and Van Der Hoek, J., A Galerkin Procedure for the Diffusion Equation Subject to the Specification of Mass, SIAM Journal on Numerical Analysis, 24(1987), 3, pp.499-515
  7. Boas, R. P., Entire Functions, Academic Press, New York, USA, 1954
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An odd entire-function solution for one-dimensional diffusion equation in theory of modular form