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IV - Powers, Exponentials, Logarithms, Trigonometric Functions
In particular, this is the case for s = -1, and since log~(x) = l/x.loga,
we conclude that the logarithmic functions are indefinitely differentiable, like
the exponential functions and powers.
These results are absolutely fundamental, even though we still lack the
most important, those concerning the functions log (without indices ... ). The
second part of this chapter will allow us to fill this gap in, and to go much
further in conjuring up a Deus ex machina: the addition formula for the
exponential series.