Geodesic
Chebyshev's alternance in the approximation of constants by simple partial fractions
Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 86-96.

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

Uniform approximation of real constants by simple partial fractions on a closed interval of the real axis is studied. It is proved that a simple partial fraction of best approximation of degree $n$ for a constant is unique and coincides with this constant at $n$ nodes lying on the interval; moreover, there is a Chebyshev alternance consisting of $n+1$ points. 
@article{TM_2010_270_a5,
     author = {V. I. Danchenko and E. N. Kondakova},
     title = {Chebyshev's alternance in the approximation of constants by simple partial fractions},
     journal = {Trudy Matematicheskogo Instituta imeni V.A. Steklova},
     pages = {86--96},
     publisher = {mathdoc},
     volume = {270},
     year = {2010},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/TM_2010_270_a5/}
}
TY  - JOUR
AU  - V. I. Danchenko
AU  - E. N. Kondakova
TI  - Chebyshev's alternance in the approximation of constants by simple partial fractions
JO  - Trudy Matematicheskogo Instituta imeni V.A. Steklova
PY  - 2010
SP  - 86
EP  - 96
VL  - 270
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/TM_2010_270_a5/
LA  - ru
ID  - TM_2010_270_a5
ER  - 
%0 Journal Article
%A V. I. Danchenko
%A E. N. Kondakova
%T Chebyshev's alternance in the approximation of constants by simple partial fractions
%J Trudy Matematicheskogo Instituta imeni V.A. Steklova
%D 2010
%P 86-96
%V 270
%I mathdoc
%U http://geodesic.mathdoc.fr/item/TM_2010_270_a5/
%G ru
%F TM_2010_270_a5
V. I. Danchenko; E. N. Kondakova. Chebyshev's alternance in the approximation of constants by simple partial fractions. Trudy Matematicheskogo Instituta imeni V.A. Steklova, Differential equations and dynamical systems, Tome 270 (2010), pp. 86-96. http://geodesic.mathdoc.fr/item/TM_2010_270_a5/

[1] Kondakova E.N., “Interpolyatsiya naiprosteishimi drobyami”, Izv. Saratov. un-ta. Matematika, mekhanika, informatika, 9:2 (2009), 50–57

[2] Macintyre A.J., Fuchs W.H.J., “Inequalities for the logarithmic derivatives of a polynomial”, J. London Math. Soc., 15 (1940), 162–168 | DOI | MR

[3] Gorin E.A., “Chastichno gipoellipticheskie differentsialnye uravneniya v chastnykh proizvodnykh s postoyannymi koeffitsientami”, Sib. mat. zhurn., 3:4 (1962), 500–526 | MR | Zbl

[4] Gelfond A.O., “Ob otsenke mnimykh chastei kornei mnogochlenov s ogranichennymi proizvodnymi ikh logarifmov na deistvitelnoi osi”, Mat. sb., 71:3 (1966), 289–296 | MR | Zbl

[5] Danchenko D.Ya., Nekotorye voprosy approksimatsii i interpolyatsii ratsionalnymi funktsiyami. Prilozhenie k uravneniyam ellipticheskogo tipa, Dis. $\dots$ kand. fiz.-mat. nauk, Vladimir. gos. ped. un-t, Vladimir, 2001

[6] Danchenko V.I., “Otsenki rasstoyanii ot polyusov logarifmicheskikh proizvodnykh mnogochlenov do pryamykh i okruzhnostei”, Mat. sb., 185:8 (1994), 63–80 | MR | Zbl

[7] Danchenko V.I., “Otsenki proizvodnykh naiprosteishikh drobei i drugie voprosy”, Mat. sb., 197:4 (2006), 33–52 | DOI | MR | Zbl

[8] Borodin P.A., “Otsenki rasstoyanii do pryamykh i luchei ot polyusov naiprosteishikh drobei, ogranichennykh po norme $L_p$ na etikh mnozhestvakh”, Mat. zametki, 82:6 (2007), 803–810 | DOI | MR | Zbl

[9] Protasov V.Yu., “Priblizheniya naiprosteishimi drobyami i preobrazovanie Gilberta”, Izv. RAN. Ser. mat., 73:2 (2009), 123–140 | DOI | MR | Zbl