Multivalued integrals

August 29th, 2007 ~ Posted in: Mathematics

How does one determine that a complex integral is multivalued? Like, without knowing that \frac{d}{dz}\log z = \frac{1}{z}, how would you know that \int \frac{1}{z} is multivalued? And, since you don’t know a closed form expression for \text{Ei}(z) = \int_z^\infty \frac{e^{-t}}{t} \; dz, how can you tell that it’s multivalued?

Mathematics ~

One Response to “Multivalued integrals”

  • 1. ObsessiveMathsFreak
    August 30th, 2007 at 12:03 pm

    I think you evaluate the integral of the function around a closed curve. If the circulation is non zero, you know there was a pole or branch point or something.

    To be honest, I think the practice is a dark art more so than a science. We are talking about integration after all.

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