Tag Archives: mathematics

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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Mathematical insult gone awry

Seen on average image board: Let’s try to solve it. The inner limit can be written as The limit in the exponent can be taken using the l’Hostpital rule The in the sense of the limit the denominator can be … 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: Green function of the two-dimensional Laplace operator

Problem Determine the Green function of the two dimensional Laplace operator Solution Recall that the Green function has to satisfy As an ansatz, we assume that depends only on the magnitude of , i.e. .  Then let us use Gauss … 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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