Geodesic
Overview of some new results concerning the theory and applications of the Rayleigh special function
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1540-1542 
M. K. Kerimov. Overview of some new results concerning the theory and applications of the Rayleigh special function. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 48 (2008) no. 9, pp. 1540-1542. http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a1/
@article{ZVMMF_2008_48_9_a1,
     author = {M. K. Kerimov},
     title = {Overview of some new results concerning the theory and applications of the {Rayleigh} special function},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {1540--1542},
     year = {2008},
     volume = {48},
     number = {9},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a1/}
}
TY  - JOUR
AU  - M. K. Kerimov
TI  - Overview of some new results concerning the theory and applications of the Rayleigh special function
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2008
SP  - 1540
EP  - 1542
VL  - 48
IS  - 9
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a1/
LA  - ru
ID  - ZVMMF_2008_48_9_a1
ER  - 
%0 Journal Article
%A M. K. Kerimov
%T Overview of some new results concerning the theory and applications of the Rayleigh special function
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2008
%P 1540-1542
%V 48
%N 9
%U http://geodesic.mathdoc.fr/item/ZVMMF_2008_48_9_a1/
%G ru
%F ZVMMF_2008_48_9_a1

Voir la notice de l'article provenant de la source Math-Net.Ru

The author's previous work provided a detailed overview of the results concerning the theory and applications of the Rayleigh special function starting from its appearance in science until recent years. Its numerous applications in various areas of mathematics, physics, and other fields were described, and an extensive bibliography was presented. This work overviews the studies not covered in the previous one and addresses new results published in many monographs and journals. Additionally, results concerning the estimation of zeros of some special polynomials and functions closely related to the Rayleigh function are described. The overview embraces the issues addressed in the scientific literature up to the last years.

[1] Kerimov M. K., “The Rayleigh function: theory and methods of its calculation”, Comput. Math. and Math. Phys., 39:12 (1999), 1883–1925 | MR | Zbl

[2] Rayleigh (Strutt J. W.), “Note on the numerical calculus of the roots of fluctuating functions”, Proc. London Math. Soc., 5 (1874), 112–194; Scientific Papers, v. 1, 1899, 190–195

[3] Watson G. N., A treatise on the theory of Bessel functions, 2nd ed., Cambridge Univ. Press, Cambridge, 1944 ; Vatson G. H., Teoriya besselevykh funktsii, Perev. s angl. B. C. Bermana, v. 1, 2, Izd-vo inostr. lit., M., 1949 | MR | Zbl

[4] Kerimov M. K., “Nekotorye zamechaniya o rabotakh, posvyaschennykh summirovaniyu ryadov s obratnymi stepenyami nulei funktsii Besselya I roda”, Zh. vychisl. matem. i matem. fiz., 47:2 (2007), 186–188 | MR | Zbl

[5] Kapitsa P. L., “Teploprovodnost i diffuziya v zhidkoi srede pri periodicheskom techenii. I. Opredelenie velichiny koeffitsienta volnovogo perenosa v trube, v scheli i v kanale”, Zh. eksperim. i teor. fiz., 21:9 (1951), 964–978

[6] Kapitsa P. L., “Vychislenie summ otritsatelnykh chetnykh stepenei kornei besselevykh funktsii”, Dokl. AN SSSR, 1951, no. 2, 561–564

[7] Meiman H. H., “O rekurrentnykh formulakh dlya stepenei summ nulei besselevykh funktsii”, Dokl. AN SSSR, 108:2 (1956), 190–193 | MR