# Talk:Regular summation methods

From Encyclopedia of Mathematics

## Riemann method regular or not?

The text states that "There are non-regular summation methods, such as [...] the Riemann summation method". On the other hand, Hardy's "Divergent series", reference [Ha], states on p.89 that the method is regular, and om p.57 makes it clear that a method is regular if it sums a convergent series to the same sum, so that the definition being used is consistent. Richard Pinch (talk) 18:15, 23 December 2014 (CET)

- Strange indeed. And moreover, our "Riemann summation method" article says that "This method was first introduced and its regularity was first proved by B. Riemann in 1854"! Boris Tsirelson (talk) 19:46, 23 December 2014 (CET)
- Another strange point is the formulation of "Riemann's second theorem" in "Riemann function"; maybe the limit is taken for $h\to0$ rather than $n\to\infty$? But no, this limit need not be 0, even if only $a_0$ is not $0$. A believable formulation of Riemann's second theorem is given in "Riemann summation method" (according to "Comments" there). Boris Tsirelson (talk) 20:01, 23 December 2014 (CET)

**How to Cite This Entry:**

Regular summation methods.

*Encyclopedia of Mathematics.*URL: http://www.encyclopediaofmath.org/index.php?title=Regular_summation_methods&oldid=35845