Geodesic
A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam
Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 115-123.

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We have considered an analytical expression for the temperature field of a semi-infinite body that is heated by a circular heat source located at the free surface. Unsteady temperature field is expressed in terms of the Appell and the Srivastava hypergeometric functions. We have studied some special areas in heated body where a non-stationary temperature field is expressed in terms of the Kampé de Fériet function. The obtained expressions have allowed to carry out the separation of the stationary and non-stationary parts of temperature field from each other. Calculations of the steady temperature fields generated by circular or Gaussian sources have been accomplished. Significant quantitative differences in these fields were not found.
Keywords: heat conductivity boundary value problem, circular heat source, hypergeometric series. 
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V. V. Manako. A representation in terms of hypergeometric functions for the temperature field in a semi-infinite body that is heated by a motionless laser beam. Journal of Samara State Technical University, Ser. Physical and Mathematical Sciences, no. 2 (2012), pp. 115-123. http://geodesic.mathdoc.fr/item/VSGTU_2012_2_a12/

[1] Pinsker V. A., “Unsteady-state temperature field in a semi-infinite body heated by a disk surface heat source”, High Temperature, 44:1 (2006), 129–138 | DOI

[2] Appel P., Kampé de Fériet J., Fonctions Hypergéométriques et Hypersphériques. Polynômes d’Hermite, Gauthier-Villars, Paris, 1926, 202 pp.

[3] Srivastava H. M., Manocha H. L., A treatise on generating functions, Halsted Press [John Wiley Sons, Inc.], New York, 1984, 569 pp. | MR | Zbl

[4] Carslaw H. S., Jaeger J. C., Conduction of Heat in Solids, Clarendon Press, Oxford, 1959, 510 pp. ; Karslou G., Eger D., Teploprovodnost tverdykh tel, Nauka, M., 1964, 488 pp. | MR

[5] Handbook of Mathematical Functions with Formulas, Graphs, and Mathematical Tables, eds. M. Abramowitz, I. A. Stegun, Dover, New York, 1972, 824 pp. ; Spravochnik po spetsialnym funktsiyam, eds. M. Abramovits, I. Stigan, Nauka, M., 1979, 832 pp. | MR | MR

[6] Prudnikov A. P. Brychkov Yu. A., Marichev O. I., Integrals and series, v. 3, Special functions. Supplementary chapters, Fizmatlit, Moscow, 2003, 688 pp. | MR

[7] Manako V. V., Putilin V. A., Kamashev A. V., “Calculation of temperature under heating by an immobile laser beam”, High Temperature, 49:1 (2011), 127–134 | DOI

[8] Srivastava H. M., Miller E. A., “A unified presentation of the Voigt functions”, Astrophys. and Space Sci., 135:1 (1987), 111–118 | DOI | MR | Zbl