92 DOC.
18
REPLY TO LAUE
[3]
After
carrying
out this
integration
and
neglecting,
in known
manner,
terms with
the
factor
1/n(v/0+n/T)
versus
those with the factor
1/n(v/0-n/T),
one
obtains
sm
1r
=
Efl
v
- -
n
I
cos
0
Y
+ 277V
- A,Vn
ß
TTlvjj
-
n
Bn
=
~
sin
7rl v
-
n
i
cos
Y +
27TV
-
Avn
0
77
(v7-"
(10)
[p.
884]
where
Xvn
=
?
+
"'
+
^v'
The formulas
(10)
are only
valid for values
t0
between
t0 =
0 and
t0
=
6
-
T
because the
expansion applies,
due to
(8), only
to
the time interval
0
-
0.
However,
we
allow ourselves to
apply
formula
(8)
to the interval 0
-
(0
+ T).
In
doing
this,
we
replace
the function
F(t)
between the time values 0 and
0
+
T with the values
of
F(t)
between
0 and
T.
This
procedure
will
falsify
our
consideration of the
mean
values,
but
only by
infinitesimal
amounts
because the time interval T
is
infinitesimal
relative to
0. Progressing
from this
observation,
we
shall
use
the
equations (10)
such
as
if
they
would be valid in the entire interval 0
t0
0.
With the
help
of
(10) we
form the
mean
value AmAn,
i.e.,
the
quantity
e
AmA"
=
-
fAmAndt.nm
m n
n
J
The
integral
e
i
o
cos
Xym
+
277/1-
0
cos
Y
+ 277V
-
Av/i
0
dt0
occurs during
this
process.
But it vanishes with
integers
\x
and
v
when
fi
=
v,
and
for
fi
=
v
it has the value
0/2
(-
l)m
-
n.
Considering
this,
the first
equation (10) yields