ABSTRACT
A singular integral equation in which L is a smooth closed contour, as well as an equation of the form
1 π
ϕ(t) t – x
dt = f (x), –∞ < x <∞, (2)
on the real axis and an equation with Cauchy kernel
1 π
ϕ(t) t – x
dt = f (x), a ≤ x ≤ b, (3)
on a finite interval, are special cases of Eq. (1). A general singular integral equation of the first kind with Cauchy kernel has the form
1 πi
∫ L
M (t, τ ) τ – t
ϕ(τ ) dτ = f (t), (4)
where M (t, τ ) is a given function. This equation can also be rewritten in a different (equivalent) form, which is given in Subsection 14.4-4.
