On the singularities of Gegenbauer (ultraspherical) expansions
On the singularities of Gegenbauer (ultraspherical) expansions
The results of Gilbert on the location of the singular points of an analytic function <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z right-parenthesis"> <mml:semantics> <mml:mrow> <mml:mi>f</mml:mi> <mml:mo stretchy="false">(</mml:mo> <mml:mi>z</mml:mi> <mml:mo stretchy="false">)</mml:mo> </mml:mrow> <mml:annotation encoding="application/x-tex">f(z)</mml:annotation> </mml:semantics> </mml:math> </inline-formula> given by Gegenbauer (ultraspherical) series expansion <inline-formula content-type="math/mathml"> <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" alttext="f left-parenthesis z …