However, there are integrals which are ( C, ? ) summable for ? > 0 which fail to converge as improper integrals ( in the sense of Riemann or Lebesgue ).
32.
As is the case with series, if an integral is summable for some value of, then it is also summable for all, and the value of the resulting limit is the same.
33.
As is the case with series, if an integral is summable for some value of, then it is also summable for all, and the value of the resulting limit is the same.
34.
More generally, the Fourier series is absolutely summable, thus converges uniformly to " f ", provided that " f " satisfies a H�lder condition of order ? > ?
35.
In fact, for any series which diverges to ( positive or negative ) infinity the Ces�ro method also leads to a sequence that diverges likewise, and hence such a series is not Ces�ro summable.
36.
The JLO cocycle is associated with a metric structure of non-commutative differential geometry known as a \ theta-summable Fredholm module ( also known as a \ theta-summable spectral triple ).
37.
The JLO cocycle is associated with a metric structure of non-commutative differential geometry known as a \ theta-summable Fredholm module ( also known as a \ theta-summable spectral triple ).
38.
Because of Fourier analysis, since the Fourier coefficients are " square-summable ", the Fourier series converges in " L " 2 which is all we need for this particular theory to function.
39.
The eta function in particular is easier to deal with by Euler's methods because its Dirichlet series is Abel summable everywhere; the zeta function's Dirichlet series is much harder to sum where it diverges.
40.
Catalan's constant occurs frequently in relation to the Clausen function, the inverse tangent integral, the inverse sine integral, the Barnes-function, as well as integrals and series summable in terms of the aforementioned functions.
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