Izv. Vyssh. Uchebn. Zaved. Mat., 2019, Number 12, Pages 71–81
On differentiation with respect to parameter of a hypergeometric function of a special type
P. L. Ivankov
Bauman Moscow State Technical University, 5/1 2-ya Baumanskaya str., Moscow, 105005 Russia
We propose an effective construction of Padé
approximation for the hypergeometric function of special type and
its derivative with respect to parameter and this parameter is
included both in numerator and denominator of the general term of
the corresponding series. The aforementioned construction has been
realized by means of a modification of the method that was applied
earlier in simpler situations. Thus obtained approximation is made
use of afterwards to establish the lower estimates of the numerical
linear forms in the values of the functions under consideration. Analagous estimates one could obtain by the known in the theory of
transcendental numbers Siegel's method but the estimates obtained by
this method would be of less exactness.
hypergeometric functions, differentiation with respect to parameter, estimates of linear forms.
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P. L. Ivankov, “On differentiation with respect to parameter of a hypergeometric function of a special type”, Izv. Vyssh. Uchebn. Zaved. Mat., 2019, no. 12, 71–81
Citation in format AMSBIB
\paper On differentiation with respect to parameter of a hypergeometric function of a special type
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
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