topic entry on series

There are in PM many entries on series whose terms are usually thought to be real but which can equally well be any complex numbers. It may be good to make a list of such entries, but of course include such ones concerning the proper complex (imaginary) term series.

1. series (http://planetmath.org/Series)

2. convergent series

3. determining series convergence

4. convergence of complex term series

5. sum of series

6. remainder term

7. finite changes in convergent series

8. manipulating convergent series

9. Riemann’s theorem on rearrangements

10. necessary condition of convergence

11. harmonic series

12. http://planetmath.org/node/11941convergent series where not only $a_n$ but also $n{a}_n$ tends to 0

13. generalization of Olivier criterion (http://planetmath.org/AGeneralisationOfOlivierCriterion)

14. slower convergent series

15. slower divergent series

16. adding and removing parentheses in series

17. absolute convergence theorem

18. limit of sequence as sum of series

19. sum of series depends on order

20. conditionally convergent real series

21. multiplication of series

22. Cauchy product

23. double series

24. absolute convergence of double series

25. Dirichlet series

26. convergence of Riemann zeta series

27. example of summation by parts

28. real part series and imaginary part series

29. sum function of series

30. termwise differentiation

31. theorems on complex function series

32. power series

33. identity theorem of power series

34. Taylor series

35. Laurent series

36. binomial theorem

37. quotient of Taylor series

38. Abel summability

39. Weierstrass double series theorem

40. infinity sum of reciprocal numbers

Title	topic entry on series
Canonical name	TopicEntryOnSeries
Date of creation	2013-03-22 17:27:59
Last modified on	2013-03-22 17:27:59
Owner	pahio (2872)
Last modified by	pahio (2872)
Numerical id	25
Author	pahio (2872)
Entry type	Topic
Classification	msc 30A99
Synonym	topic entry on series of complex terms