## New answers tagged power-series

3
votes

### Reference request for Bessel function of the second kind with matrix argument

Because Bessel functions of the first and second kind are related by
$$Y_\nu(z)=\frac{J_\nu(z)\cos\pi\nu-J_{-\nu}(z)}{\sin \pi\nu},$$
you can refer to literature that studies the function $J_\nu$ with ...

1
vote

### How to express a quadratic polynomial exactly as a power series

[This answers the question as originally stated. It has now been changed.]
Given the series expansion
$$1+b_1\arctan x+b_2 \arctan^2 x=1+\sum_{k=1}^\infty a_k x^k$$
one has the relationships
$$a_{2k+...

2
votes

Accepted

### Confusion regarding $\ln \omega$

The exponentiation in $\omega^{\frac{1}{\omega}} = \ln \omega$ is not that given by the exponential function. It is the value at $\frac{1}{\omega}$ of Conway's $\omega$-map.

44
votes

Accepted

### Does every series of hyperreal numbers converge to some hyperreal number?

The answer is strongly negative.
Arbitrary extensions. The first thing to say is that whenever one extends $\newcommand\R{\mathbb{R}}\R$ to a larger ordered field $F$, one has immediately destroyed (...

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