Skip to main content

New answers tagged

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 ...
Carlo Beenakker's user avatar
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+...
Carlo Beenakker's user avatar
2 votes

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.
nombre's user avatar
  • 2,417
44 votes

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 (...
Joel David Hamkins's user avatar

Top 50 recent answers are included