for Gudermanian and its Inverse.
in (49), (48) their expansions, Art. 16, and integrate, then
No constants of integration appear, since
. These series are seldom
used in computation, as
is best found and tabulated by means of tables of natural tangents and hyperbolic
sines, from the equation
and a table of the direct function can be used to furnish the numerical values
of the inverse function; or the latter can be obtained from the equation,
To obtain a logarithmic expression for
- Evaluate ,
- Prove that
is an inﬁnitesimal of the ﬁfth order, when .
- Prove the relations ,