It remains to calculate the integrals along \(\mathcal {C}_{2}, \mathcal {C}_{4}\) .
To this end, we choose
\(s = D x^{2} e^{i \pi }\) 
and use [1]}
\(I_{n}(xe^{\pm \pi i/2}) &=& e^{\pm n\pi i/2} J_{n}(x), \\K_{n}(xe^{\pm \pi i/2}) &=& \pm \frac{1}{2}\pi i e^{\mp n\pi i/2} [-J_{n}(x) \pm i Y_{n}(x)].\) 

Осталось вычислить интегралы вдоль \(\mathcal {C}_{2}, \mathcal {C}_{4}\).

Для этого выберем

\(s = D x^{2} e^{i \pi}\)

и используем [1]}

\(I_{n}(xe^{\pm \pi i/2}) &=& e^{\pm n\pi i/2} J_{n}(x), \\K_{n}(xe^{\pm \pi i/2}) &=& \pm \frac{1}{2}\pi i e^{\mp n\pi i/2} [-J_{n}(x) \pm i Y_{n}(x)].\)