We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
$F_1$
Liu [‘Supercongruences for truncated Appell series’, Colloq. Math. 158(2) (2019), 255–263] and Lin and Liu [‘Congruences for the truncated Appell series 
$F_3$ and 
$F_4$’, Integral Transforms Spec. Funct. 31(1) (2020), 10–17] confirmed four supercongruences for truncated Appell series. Motivated by their work, we give a new supercongruence for the truncated Appell series 
$F_{1}$, together with two generalisations of this supercongruence, by establishing its q-analogues.
We study the problem of determining the holomorphic self maps of the unit disc that induce a bounded composition operator on Dirichlet-type spaces. We find a class of symbols 
$\varphi $ that induce a bounded composition operator on the Dirichlet-type spaces, by applying results of the multidimensional theory of composition operators for the weighted Bergman spaces of the bi-disc.