Geodesic
The Bloch–Gruneisen function of arbitrary order and its series representations
Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 44-50
Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

We derive several series representations for the Bloch–Gruneisen function of an arbitrary (integer or noninteger) order and show that it is related to other, more familiar special functions more commonly used in mathematical physics. In particular, the Bloch–Gruneisen function of integer order is expressible in terms of the Bose–Einstein function of different orders
Keywords: Bloch–Gruneisen formula, Bloch–Gruneisen function, Bose–Einstein function, incomplete gamma function, electrical resistivity.
Mots-clés : Debye function, polylogarithm 
@article{TMF_2011_166_1_a2,
     author = {D. Cvijovi\'c},
     title = {The~Bloch{\textendash}Gruneisen function of arbitrary order and its series representations},
     journal = {Teoreti\v{c}eska\^a i matemati\v{c}eska\^a fizika},
     pages = {44--50},
     year = {2011},
     volume = {166},
     number = {1},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a2/}
}
TY  - JOUR
AU  - D. Cvijović
TI  - The Bloch–Gruneisen function of arbitrary order and its series representations
JO  - Teoretičeskaâ i matematičeskaâ fizika
PY  - 2011
SP  - 44
EP  - 50
VL  - 166
IS  - 1
UR  - http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a2/
LA  - ru
ID  - TMF_2011_166_1_a2
ER  - 
%0 Journal Article
%A D. Cvijović
%T The Bloch–Gruneisen function of arbitrary order and its series representations
%J Teoretičeskaâ i matematičeskaâ fizika
%D 2011
%P 44-50
%V 166
%N 1
%U http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a2/
%G ru
%F TMF_2011_166_1_a2
D. Cvijović. The Bloch–Gruneisen function of arbitrary order and its series representations. Teoretičeskaâ i matematičeskaâ fizika, Tome 166 (2011) no. 1, pp. 44-50. http://geodesic.mathdoc.fr/item/TMF_2011_166_1_a2/

[1] J. M. Ziman, Electrons and Phonons, Clarendon Press, Oxford, 2001 | Zbl

[2] J. Bass, W. P. Pratt Jr., P. A. Schroeder, Rev. Modern Phys., 62:3 (1990), 645–744 | DOI

[3] S. S. Kubakaddi, Phys. Rev. B, 75:7 (2007), 075309, 7 pp. | DOI

[4] A. Bid, A. Bora, A. Raychaudhuri, Phys. Rev. B, 74:3 (2006), 035426, 8 pp., arXiv: cond-mat/0607674 | DOI

[5] L. Mazov, Phys. Rev. B, 70:5 (2004), 054501, 5 pp. | DOI

[6] J. Shen, M. Fang, Y. Zheng, H. Wang, Y. Lu, Z. Xu, Physica C, 386 (2003), 663–666 | DOI

[7] H. Takagi, B. Batlogg, H. L. Kao, J. Kwo, R. J. Cava, J. J. Krajewski, W. F. Peck Jr., Phys. Rev. Lett., 69:20 (1992), 2975–2978 | DOI

[8] D. Varshney, N. Kaurav, J. Low Temper. Phys., 141:3–4 (2005), 165–178 | DOI

[9] M. Abramovits, I. Stigan (red.), Spravochnik po spetsialnym funktsiyam s formulami, grafikami i matematicheskimi tablitsami, Nauka, M., 1979 | MR | MR | Zbl

[10] B. S. Pavlov, L. D. Faddeev, “Teoriya rasseyaniya i avtomorfnye funktsii”, Kraevye zadachi matematicheskoi fiziki i smezhnye voprosy teorii funktsii. 6, Zap. nauchn. sem. LOMI, 27, Izd-vo “Nauka”, Leningrad. otd., L., 1972, 161–193 | MR | Zbl

[11] Yu. V. Matiyasevich, Hidden life of Riemann's zeta function 1. Arrow, bow, and targets, arXiv: 0707.1983

[12] Yu. V. Matiyasevich, Hidden life of Riemann's zeta function 2. Electrons and trains, arXiv: 0709.0028

[13] M. V. Berry, Nonlinearity, 21:2 (2008), T19–T26 | DOI | MR | Zbl

[14] M. V. Berry, J. P. Keating, SIAM Rev., 41:2 (1999), 236–266 | DOI | MR | Zbl

[15] L. Lewin, Polylogarithms and Associated Functions, North-Holland, New York, 1981 | MR | Zbl

[16] D. Cvijović, Proc. R. Soc. Lond. Ser. A, 463:2080 (2007), 897–905, arXiv: 0911.4452 | DOI | MR | Zbl

[17] Y. Igasaki, H. Mitsuhashi, Phys. Status Solidi A, 99:2 (1987), K111–K115 | DOI

[18] M. Deutsch, J. Phys. A, 20:13 (1987), L811–L813 | DOI

[19] S. Paszkowski, Numer. Algorithms, 20:4 (1999), 369–378 | DOI | MR | Zbl

[20] B. A. Mamedov, I. M. Askerov, Phys. Lett. A, 362:4 (2007), 324–326 | DOI

[21] D. Svizhovich, TMF, 161:3 (2009), 400–405 | DOI | MR | Zbl