An algorithm of the calculation of derivatives of an implicit function
Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 3, pp. 849-861
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A method of the formalization of the expression for high derivatives of an implicit function is suggested. An algorithm of the calculation of these expressions by the computer is constructed. As an example, the equation $J_{\nu}(x)=0$ is considered where $J_{\nu}(x)$ is the Bessel function of index $\nu$; its solutions $\nu=\nu(x)$ are approximated by the Taylor's polynomial. The coefficients of the approximation are calculated for the first five zeros and the precision of the approximating formulas is examined numerically.
@article{FPM_1996_2_3_a6,
author = {I. B. Kozhukhov and N. I. Platonov and A. A. Prokof'yev},
title = {An algorithm of the calculation of derivatives of an implicit function},
journal = {Fundamentalʹna\^a i prikladna\^a matematika},
pages = {849--861},
publisher = {mathdoc},
volume = {2},
number = {3},
year = {1996},
language = {ru},
url = {http://geodesic.mathdoc.fr/item/FPM_1996_2_3_a6/}
}
TY - JOUR AU - I. B. Kozhukhov AU - N. I. Platonov AU - A. A. Prokof'yev TI - An algorithm of the calculation of derivatives of an implicit function JO - Fundamentalʹnaâ i prikladnaâ matematika PY - 1996 SP - 849 EP - 861 VL - 2 IS - 3 PB - mathdoc UR - http://geodesic.mathdoc.fr/item/FPM_1996_2_3_a6/ LA - ru ID - FPM_1996_2_3_a6 ER -
%0 Journal Article %A I. B. Kozhukhov %A N. I. Platonov %A A. A. Prokof'yev %T An algorithm of the calculation of derivatives of an implicit function %J Fundamentalʹnaâ i prikladnaâ matematika %D 1996 %P 849-861 %V 2 %N 3 %I mathdoc %U http://geodesic.mathdoc.fr/item/FPM_1996_2_3_a6/ %G ru %F FPM_1996_2_3_a6
I. B. Kozhukhov; N. I. Platonov; A. A. Prokof'yev. An algorithm of the calculation of derivatives of an implicit function. Fundamentalʹnaâ i prikladnaâ matematika, Tome 2 (1996) no. 3, pp. 849-861. http://geodesic.mathdoc.fr/item/FPM_1996_2_3_a6/