The infinite series
R
p
=
∑
k
=
1
∞
(
2
k
−
1
)
−
p
x
2
k
−
1
R_p = \sum _{k=1}^\infty {(2 k - 1)}^{- p} \, x^{2 k - 1}
,
0
>
1
−
x
≪
1
0 >1-x\ll 1
,
p
=
2
p = 2
or
3
3
, and the related series
C
(
x
,
b
,
2
)
a
m
p
;
=
∑
k
=
1
∞
(
2
k
−
1
)
−
2
cosh
(
2
k
−
1
)
x
/
cosh
(
2
k
−
1
)
b
,
0
>
1
−
x
/
b
≪
1
,
S
(
x
,
b
,
3
)
a
m
p
;
=
∑
k
=
1
∞
(
2
k
−
1
)
−
3
sinh
(
2
k
−
1
)
x
/
cosh
(
2
k
−
1
)
b
,
\begin{equation*} \begin {split} C(x,b,2) &=\sum _{k=1}^\infty {(2k-1)}^{-2} \cosh (2k-1)x/\cosh (2k-1)b,\quad 0 >1-x/b \ll 1,\\ S(x,b,3)&=\sum _{k=1}^\infty {(2k-1)}^{-3} \sinh (2k-1)x/\cosh (2k-1)b, \end{split} \end{equation*}
are of interest in problems concerning contact between plates and unilateral supports. This article will re-examine a previously published result of Baratella and Gabutti for
R
p
R_p
, and will present new, rapidly convergent, series for
C
(
x
,
b
,
2
)
C(x,b,2)
and
S
(
x
,
b
,
3
)
.
S(x,b,3).