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I am looking for examples of how contour line integrals may be used to prove certain identities (that may seem unrelated to complex analysis) like this combinatoric one. Can anyone suggest more examples or links to them?

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    $\begingroup$ See Egorychev Method. In addition, you can visit the @Marko Riedel MSE page: He has many examples which are related to your question. $\endgroup$ – Felix Marin Apr 30 '17 at 4:16
  • $\begingroup$ @Felix Marin your links are both interesting and illustrative. I was unaware until now that a systematic study of this method had been undertaken. $\endgroup$ – T.A.Tarbox May 3 '17 at 1:05
  • $\begingroup$ @Felix Marin I wonder if it is at all possible to generalize this method to prove q-analogues of binomial identities. I think it's worth the effort to investigate this possibility. $\endgroup$ – T.A.Tarbox May 3 '17 at 1:22

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