Title: Singular Integral Equations: Boundary Problems of Function Theory and Their Application to Mathematical Physics Author: N. I. Muskhelishvili (also spelled Muskhelishvili) Original Russian Publication: 1946 (frequently revised) English Translation: 1953 (P. Noordhoff, Groningen; later Dover reprints)
[ \kappa = \frac12\pi \left[ \arg G(t) \right]_\Gamma. ] \textP.V. \int_\Gamma \frac\phi(t)t-t_0
where P.V. denotes the Cauchy principal value. The singular integral operator \textP.V. \int_\Gamma \frac\phi(t)t-t_0
[ \Phi(z) = \frac12\pi i \int_\Gamma \frac\phi(\tau)\tau-z , d\tau, ] \textP.V. \int_\Gamma \frac\phi(t)t-t_0
[ \Phi^\pm(t_0) = \pm \frac12 \phi(t_0) + \frac12\pi i , \textP.V. \int_\Gamma \frac\phi(t)t-t_0 , dt, ]