The integral: $$S(x)=\int_0^x H^{(1)}_{k+1}(\eta)H^{(2)}_{k-1}(\eta)d\eta$$ can be expressed as a combination of Hypergeometric functions and trigonometric functions. I have some difficulty to calculate the previous integral $S(x)$ defined between $0$ and $+\infty$. Can someone give me any hint? Thanks
2026-04-29 09:39:14.1777455554
Integral of Hankel functions
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