Tag Archives: math

Let gooby do teh hoemwerk: Riemann zeta at two

Based on what I read in a very old book, we show We can divide the sum into even and odd contributions One sees that In order to evaluate the right hand side of this equation we consider the function … Continue reading

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Pade approximants: a case study (iii)

We are now going to explore the analytic structure of the Padé approximants for our example [1], [2]. The study (iii) The limit for the Padé approximants and  exist for all . This is much stronger than the Taylor series, … Continue reading

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Pade approximants: a case study (ii)

In the previous article we have seen how to calculate Padé approximations on the example of The study (ii) We are now going to see how efficient Padé’s ansatz is and compare it to the well known series representation . … Continue reading

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Pade approximants: a case study (i)

This post was inspired by a lecture series of Carl Bender [1]. The case I will consider the function on the complex plane, defined by Have a look at a complex plot of it Some properties: has a a logarithmic … Continue reading

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Let gooby do teh hoemwerk: Baker-Campbell-Hausdorff identities

Problem Let and be linear operators, which commute with the commutator of and , i.e. Show that the following formulae hold: which are known as the Baker-Campbell-Hausdorff identities. They play an important rule, e.g. in quantum mechanics, whenever one deals … Continue reading

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Let gooby do teh hoemwerk: Sokhatsky-Weierstrass identity

Problem The Sokhatsky-Weierstrass identity provides a simple formula for , i.e. a simple pole that is shifted slightly to the lower half of the complex plane. It holds in the sense of distributions: where stands for the Cauchy principal value. … Continue reading

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