Principal-value and finite-part integrals

For a function f E Co@ [a, b] a Cauchy principal-value integral is defined by

For f E C1>"[a, b] a two-sided Hadamard finite-part integral of order two is defined by

b f ( t ) dt 2f ( l } f It) t = lii ' A@- (S - t)2 dt +

(C.4)

270 C. PRINCIPAL-VA L UE AND FINITE-PART INTEGRALS

which has the regularization