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Results tagged with reference-request
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user 106114
This tag is used if a reference is needed in a paper or textbook on a specific result.
5
votes
Non-commutativity of the d'alambert operator acting on the covariant derivative of a scalar ...
Use
$$
[\nabla_\mu,\nabla_\nu]V^\rho=R_{\mu\nu}{}^{\rho\sigma} V_\sigma
$$
to conclude that
$$
\begin{aligned}
{}[\nabla^\nu\nabla_\nu,\nabla_\mu]\phi&\overset{ \mathrm A}=\nabla^\nu[\nabla_\nu,\nabla …
8
votes
Does this multiplicative function have a name? If so, what is known about it?
This is also called the Dedekind $\psi$ function:
$$
\psi(n):=n\prod_{p|n}(1+p^{-1})
$$
See also A001615 and A158523.
10
votes
A special type of generating function for Fibonacci
Perhaps interesting to note the following.
In the notation of Henri Cohen,
$$
F(x)=1 + x+\frac{x^2}{\color{red} 2}-\frac{x^3}{\color{red} 3}+\frac{x^4}{\color{red}8}+\frac{x^5}{15}-\frac{25 x^6}{\col …