AN ANHARMONIC FOURIER ANALYSIS FOR USE IN PROBLEMS OF HEAT CONDUCTION AND MEIJER'S G-FUNCTION

Authors

  • S. D. Bajpai Department of.mathematics, University of Bahrain, P.O. Box 32038, Isa Town, BAHRAIN.
  • Sadhana Mishra 11, Sardarpura, Udaipur, INDIA.

DOI:

https://doi.org/10.5556/j.tkjm.21.1990.4665

Keywords:

anharmonic Fourier analysis, heat conduction, Meijer’s G-function

Abstract

In this paper, we develop a.n anharmonic Fourier analysis for use in problems of heat conduction. We also evaluate an integral involving Meijer's G- function and show how Meijer's G-function can be utilized to solve a problem of heat conduction in a rod under boundary conditions of special kind with the help of our anharmonic Fourier analysis.

References

Bajpai, S. D. Use of Gauss's hypergeometric functions and Meijer's G-function is the production of heat in a cylinder. Proc. Camb. Phil. Soc. 64, (1968), 1049-1054.

Bajpai, S. D. The use of Meijer's G-frmction in the electrostatic field between two spherical conduc- tors. J. Sci. Engg. Res. XIII-I, (1969), 149-152.

Bajpai, S. D. Meijer's G-function and temperature in a slab with faces at temperature zero. J. Sci. Engg. Res. XIII-2, (1969), 254-257.

Bajpai, S. D. The potential about a spherical surface and Meijer's G-function, Vijnana Parishad Anusandhan Patrika, 12(11), (1969), 93-97.

Bajpai, S. D. Meijcr's G-function and the temperature in a non-homogeneous bar. Proc. Indian Acad. Sci. LXX, (1969), 697-701.

Bajpai, S. D. Special functions and forced synunetrical vibrations in a circular elastic plate. Proc. Comb. Phi. Soc. 66, (1969), 349-353.

Bajpai, S. D. An integral involving Fox's H-function and heat conduction. Math. Education Sect A, 7, (1969), 1-4.

Bajpai, S. D. Fox's H-fuction and temperature in a slab with insulated faces. Jour. Math. Phys. Sci. 4, (1970), 302-307.

Bajpai, S. D. Meijer's G-function and angular displacement in a shaft. Proc. Nat. Acad. Sci. India, 41 (A), (1971), 320-231.

Bajpai, S. D. Meijer's G-function and temperature in a slab with thermally insulated faces. Proc. Int. Con. Num. Method. in Thermal problems II, (1981), 677-683.

B·ajpai, S. D. Fox's H-function and temperature in a non-homogenious bar. Proc. Int. Con. Num. Method in Thermal Problems III, (1983), 239-341.

Bajpai, S. D. Fox's H-function and angular twist in a shaft. Proc. SAMSA Symposium V, (1986), 122-131.

Carslaw, H. S. and Jaeger, J. C. Conduction of heat in solids. Clarendon Press, Oxford, (1986).

Erdelyi, A. et al. Higher transcendental functions, Vol.1. McGraw Hill, New York, (1953).

Erdelyi, A. et al. Tables of Integral transforms, Vol.2. McGraw Hill, (1954).

Gradshteyn, L. S. and Ryzhik, I. M. Tables of Integrals, series and products. Academic Press, Inc., New York, (1980).

Kalla, S. K. and Kushwaha, R. S. Production of heat in a cylinder. Acta Mexicana Cien. Teen. 4, (1970), 89-93.

Mathai, A. M. and Saxena, R. K. Lecture Notes in Maths. 348-Generalized hypergeometric functions with applications in statistics and physical sciences. Springer-Verlag Berlin, Heidelberg, (1973).

Mathai, A. M. and Saxena, R. K. The H-function with applications in statistics and other disciplines. Wiley Eastern Ltd, New Delhi, (1978). .

Prasad, Y. N. and Siddiqui, A. Application of generalized function in the production of heat in a cylinder. Defence Sci. J. 25, (1975), 107-114.

Prasad, Y. N. and Siddiqui, A. Application of generalized functions of two variables in vibrations of a circular memberance. Vijnana Parishad Anusandhan Patrika 20, (1977), 113-122.

Prasad, Y. N. and Singh, S. N. An application of the H-function of several complex variables in the production of heat in a cylinder. Pure Appl. Math. Sci. 6, (1977), 57-64.

Shah, M. Heat conduction, generalized Meijer function and Hermite polynomials. Comment Math. Univ. St. Paul. 18, (1970), 81-94.

Shah, M. On generalized Meijer function of two variables and some applications. Comment. Math. Univ. St. Paul 19, (1970), 93-122.

Sharma, O. P. H-function and heat production in a cylinder. Proc. Nat. Acad. Sci. India, Sect. A,39, (1969), 355-360.

Singh, F. and Vanna, R. C. Application of E-operator to evaluate a definite integral and its application in heat condition. J. Indian Math. Soc. 36, (1972), 325-332.

Srivastava, H. M. , Gupta, K. C. and Goyal, S. P. The H-function of one and two variables with applications. South Asian Publishers, New Delhi, (1982).

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Published

1990-09-01

How to Cite

Bajpai, S. D. . ., & Mishra, S. (1990). AN ANHARMONIC FOURIER ANALYSIS FOR USE IN PROBLEMS OF HEAT CONDUCTION AND MEIJER’S G-FUNCTION. Tamkang Journal of Mathematics, 21(3), 215–222. https://doi.org/10.5556/j.tkjm.21.1990.4665

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Papers