Meromorphic Reduction in Integration

It is argued that for certain meromorphic functions $u:\cal{R}\rightarrow\cal{R}$ and analytic function $ A_1$ and for any integrable function $F$, as long as it converges as a Cauchy Principal Value,, $$\int_{-\infty}^{\infty}A_1(x)F[u(x)] dx=\int_{-\infty}^{\infty} A_2(x)F(x) dx,$$ where $A_2$ is also analytic.

💡 Research Summary

The paper “Meromorphic Reduction in Integration” by Lawrence Glasser introduces a broad generalization of the classic Cauchy‑Schlomilch identity, which states that for a suitably integrable real‑valued function F, the Cauchy principal value of
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