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On the Khintchine constant for centred continued fraction expansions.

In this note, we consider a classical constant that arises in number theory, namely the Khintchine constant. This constant is closely related to the growth of partial quotients that appear in continued fraction expansions of reals. It equals the limit of the geometric mean of the partial quotient which is proved to be the same for almost all real numbers. We provide several expressions for this constant in the particular case of centred continued fraction expansions as well as a numerical evaluation of this constant up to 1000 digits.