Geodesic
Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions
Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 186-188 
M. K. Kerimov. Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions. Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki, Tome 47 (2007) no. 2, pp. 186-188. http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a1/
@article{ZVMMF_2007_47_2_a1,
     author = {M. K. Kerimov},
     title = {Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind {Bessel} functions},
     journal = {\v{Z}urnal vy\v{c}islitelʹnoj matematiki i matemati\v{c}eskoj fiziki},
     pages = {186--188},
     year = {2007},
     volume = {47},
     number = {2},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a1/}
}
TY  - JOUR
AU  - M. K. Kerimov
TI  - Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions
JO  - Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
PY  - 2007
SP  - 186
EP  - 188
VL  - 47
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a1/
LA  - ru
ID  - ZVMMF_2007_47_2_a1
ER  - 
%0 Journal Article
%A M. K. Kerimov
%T Some remarks on works concerning the summation of series with inverse powers of zeros of first-kind Bessel functions
%J Žurnal vyčislitelʹnoj matematiki i matematičeskoj fiziki
%D 2007
%P 186-188
%V 47
%N 2
%U http://geodesic.mathdoc.fr/item/ZVMMF_2007_47_2_a1/
%G ru
%F ZVMMF_2007_47_2_a1

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

Some recent works related to the Rayleigh function are analyzed that reestablish results that have been known in the literature for over one hundred years.

[1] Berestovskii G. N., “Ob odnom svoistve nulei funktsii Besselya $J_0(\mu)$”, Matem. zametki, 75:2 (2004), 302 | MR | Zbl

[2] Beilin C. A., “Ob odnom svoistve kornei funktsii Besselya $J_\nu(x)$”, Vestn. Samarskogo gos. tekhn. un-ta, 2004, no. 30, 186–187

[3] Tikhonov A. N., Samarskii A. A., Uravneniya matematicheskoi fiziki, Nauka, M., 1966 | MR | Zbl

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

[5] Vatson T. N., Teoriya besselevykh funktsii, v. 1, Izd-vo inostr. lit., M., 1949, Perev. s angl. B. C. Bermana

[6] Kerimov M. K., “Funktsiya Releya – teoriya i metody vychisleniya”, Zh. vychisl. matem. i matem. fiz., 39:12 (1999), 1962–2006 | MR | Zbl

[7] Volynskaya M. G., “O razreshimosti odnoi nelokalnoi zadachi s integralnym usloviem”, Matem. modelirovanie i kraevye zadachi. Ch. 3. Differents. ur-niya i kraevye zadachi, Tr. II Vseros. nauchn. konf. (Samara, 1–3 iyunya, 2005), Samara, 2005, 62–64

[8] Kerimov M. K., “O vychislenii funktsii Releya”, Analitich. i chisl. metody resheniya zadach matem. fiz., ed. A. A. Abramov, VTs AN SSSR, M., 1989, 109–116 | MR

[9] 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

[10] Kapitsa P. L., “Vychislenie summ otritsatelnykh chetnykh stepenei kornei besselevykh funktsii”, Dokl. AN SSSR, 77:4 (1951), 561–564

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