### ON SOME RELATIONS CONNECTING FLUID DYNAMICS AND BI-COMPLEX ANALYSIS

#### Abstract

In the paper our main target is to derive some results focusing some connection between fluid dynamics and bi-complex analysis which in fact is the most recent mathematical tool to develop the theory of complex analysis.** **

**AMS Subject Classification (2010)**: 30D30,30D35, 76A02.

**Keywords and Phrases**: Potential fluid flow, ψ-order ( ψ-lower order), ψ– zero order ( ψ-zero lower order),bicomplex number,bicomplex potential, composition, growth indicators, idempotent representation, factorization.

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G. B. Price : An introduction to multiplex spaces and functions, Marcel Dekker Inc., New York, 1991.

Michiji Futagawa : On the theory of functions of a quaternary variable, Tȏhoku Math. J. Vol. 29 (1928), pp. 175-222 ; Vol. 35 (1932), pp. 69-120.

E. Hille : Analytic Function Theory, Chelsea Publishing, New York, Vol. I (1982), xi+308 pp.; Vol. II (1977), xii+496 pp.

James D. Riley : Contributions to the theory of functions of a bicomplex variable, Tȏhoku Math. J. 2nd series, Vol. 5 (1953), pp. 132-165.

G. K. Batchelor : An introduction to fluid dynamics, Cambridge Mathematical Library (1967).

J. Clunie : The composition of entire and meromorphic functions, Mathematical Essays dedicated to A. J. Macintyre, Ohio University Press (1970), pp. 75-92.

L. Liao and C.C. Yang : On the growth of composite entire functions, Yokohama Math. J., Vol. 46 (1999), pp. 97-107.

J. Rauch : Some fluid flows, Applied Complex Analysis (Ref. Website : www.math.1sa.umich.edu).

C. Segre : Le rappresentazionirealedelleformecomplesse’sGliEntiIperalgebrici, Math. Ann., Vol. 40 (1892), 413-467.

G. Valiron : Lectures on the general theory of integral functions, Chelsea Publishing Company (1949).

T. Yokoyama : Fluid Mechanics, Topology and Complex Analysis ( Ref.Websitewww.stat.phys.titech.ac.jp/yokoyama/note 4.pdf ).

G. D. Song and C. C. Yang : Further growth properties of composition of entire and meromorphic functions, Indian J. Pure Appl. Math, Vol. 15 (1984) No. 1, pp. 67-82.

K. S. Charak and D. Rochon : On factorization of bicomplex meromorphic functions, Quarternionic and Clifford Analysis, Trends in Mathematics, pp. 55-68© 2008 BirkhäuserVerlag Basel/Switzerland.

S. K. Datta and T. Biswas : On some further results of growth properties of composite entire and meromorphic functions, Int. Journal of Math. Analysis, Vol. 3, No. 29 (2009), pp. 1413-1428.

S. K. Datta and P. Sen : Deduction of some relations connecting Bicomplex Analysis and Fluid Dynamics, Int. J. of Adv. Sci. & Tech. Research, Issue 3, Vol. 3, May-June 2013, pp. 60-69.

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