Explicit Form of Asymptotic Coefficients in a Reentrant Corner for Conformal Mapping of an L-Shaped Domain

For the conformal mapping of an L-shaped domain with ledges of arbitrary length $$A$$ and width $$h$$ and a reentrant corner of size $$\pi \beta $$ , we find explicit analytical formulas for the expansion coefficients $${{c}_{n}}$$ of the mapping function near the vertex $${{w}_{1}}$$ of the reentrant corner. The formulas for $${{c}_{n}}$$ , which are known as stress intensity factors (SIFs), are derived in the form of series in powers of the small parameter $$\delta : = \exp ( - \pi A{\text{/}}h)$$ with coefficients determined only by $$\beta $$ using explicit formulas. A brief bibliographic survey concerning the problem of calculating SIFs is given.