The results of Gilbert on the location of the singular points of an analytic function
f
(
z
)
f(z)
given by Gegenbauer (ultraspherical) series expansion
f
(
z
)
=
Σ
n
=
0
∞
a
n
C
n
μ
(
z
)
f(z)\, = \,\Sigma _{n\, = \,0}^\infty \,{a_n}\,C_n^\mu (z)
are extended to the case where the series converges to a distribution. On the other hand, this generalizes Walter’s results on distributions given by Legendre series:
f
(
z
)
=
Σ
n
=
0
∞
a
n
C
n
1
/
2
(
z
)
f(z)\, = \,\Sigma _{n\, = \,0}^\infty \,{a_n}\,C_n^{1/2}(z)
. The singularities of the analytic representation of
f
(
z
)
f(z)
are compared to those of the associated power series
g
(
z
)
=
Σ
n
=
0
∞
a
n
z
n
g(z)\, = \,\Sigma _{n\, = \,0}^\infty \,{a_n}{z^n}
. The notion of value of a distribution at a point is used to study the boundary behavior of the associated power series. A sufficient condition for Abel summability of Gegenbauer series is also obtained in terms of the distribution to which the series converges.