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Only a few terms are needed to evaluate Ewald sums, which are cast in terms of error functions and exponential integrals, to high accuracy.
We define some finite sums which are associated with the Dedekind type sums and Hardy-Berndt type sums.
In Section 2, we define some new finite arithmetic sums which are associated with the Dedekind sums, the Hardy-Berndt sums, and Simsek's sum.
While both ordinary objects and sums (which are also objects) exist, they cannot be identical, since the clay can both pre-exist the statue it constitutes, and can survive past the statue being crushed.
In this section, we define some new finite sums which are related to not only the functions [ x ] and ( ( x ) ), but also the Dedekind sums, the Hardy-Berndt sums, the Simsek sum Y ( h, k ), and the other finite sums.
Very recently, Srivastava presented a systematic investigation of numerous interesting properties of some families of generating functions and their partial sums which are associated with various classes of the extended Hurwitz-Lerch zeta functions.
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So in the 1988 presidential race, big donors were back, exploiting this loophole to give unregulated sums, which were labeled soft money.
I was in Japan making a radio documentary about numeracy, Land of the Rising Sums, which was broadcast on BBC Radio 4 at 11am on Monday 29 October.
And it's because Live Nation has been paying the acts these outrageous sums, which is just alienating the fan base".
The corporate tap seemed to have been turned off, and also people had stopped giving those ad hoc sums which were so important to us.
He's against them being quickly sold for lump sums, which is the option preferred by the Mayor's Office for Policing and Crime, albeit with one or two interesting exceptions.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com