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 $na_{n}$ 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

单词	TopicEntryOnSeries
释义	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 $na_{n}$ 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
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