Residue theorem | Wikipedia audio article
Channel: wikipedia tts
Date: 29/12/2018

This is an audio version of the Wikipedia Article:
https://en.wikipedia.org/wiki/Residue_theorem


00:00:31 1 Statement
00:03:19 2 Examples
00:05:29 2.1 An integral along the real axis
00:05:38 2.2 An infinite sum
00:07:51 3 See also
00:17:35 4 References
00:17:45 5 External links
00:20:51 iz/1 − e−iz − iz/2.) Thus, the residue Resz
00:24:24 See also



Listening is a more natural way of learning, when compared to reading. Written language only began at around 3200 BC, but spoken language has existed long ago.

Learning by listening is a great way to:
- increases imagination and understanding
- improves your listening skills
- improves your own spoken accent
- learn while on the move
- reduce eye strain

Now learn the vast amount of general knowledge available on Wikipedia through audio (audio article). You could even learn subconsciously by playing the audio while you are sleeping! If you are planning to listen a lot, you could try using a bone conduction headphone, or a standard speaker instead of an earphone.

Listen on Google Assistant through Extra Audio:
https://assistant.google.com/services/invoke/uid/0000001a130b3f91
Other Wikipedia audio articles at:
https://www.youtube.com/results?search_query=wikipedia+tts
Upload your own Wikipedia articles through:
https://github.com/nodef/wikipedia-tts
Speaking Rate: 0.8031025879619506
Voice name: en-AU-Wavenet-C


"I cannot teach anybody anything, I can only make them think."
- Socrates


SUMMARY
=======
In complex analysis, a discipline within mathematics, the residue theorem, sometimes called Cauchy's residue theorem, is a powerful tool to evaluate line integrals of analytic functions over closed curves; it can often be used to compute real integrals and infinite series as well. It generalizes the Cauchy integral theorem and Cauchy's integral formula.  From a geometrical perspective, it is a special case of the generalized Stokes' theorem.