# Tag Info

1 vote

### Hermite's identity for sum of floor function

Assume that a function $f$ is given as a power series $$f(x) = A_0 + A_1x + A_2x^2 + \ldots;$$ then $$\frac{f(x)}{1-x} = A_0 + (A_0+A_1)x + (A_0 + A_1 + A_2)x^2 + \ldots$$ as can be verified ...
1 vote

### Why are the trig functions versine, haversine, exsecant, etc, rarely used in modern mathematics?

It’s true that those functions are rarely used today for the reasons set out above. But, they are still used. For example, there are many yachts cruising around the world and while most, if not all, ...
Accepted

### Did Newton and Leibniz use limits in their derivations of differential calculus?

Newton and Leibniz initially expressed the derivative $f'(x)$ as the ratio $\frac{df}{dx}$, where the rates of change $df$ and $dx$ are infinitesimal numbers. Analogously, the integral was defined as ...
1 vote

### How to prove an identity of Gauss for the logarithm of Jacobi theta function?

I somehow missed that trick in my previous attempts but franz lemmermeyer's useful comment was a sort of guidance that made it clear to me how to resolve this question. Lets look at the seperate cases ...
1 vote

### How to prove an identity of Gauss for the logarithm of Jacobi theta function?

This is not an answer and I've got to run. Take $n$ odd; then  \frac{2q^n - q^{2n}}{1-q^{2n}} = \frac{2q^n - 2q^{2n}}{1-q^{2n}} + \frac{q^{2n}}{1-q^{2n}} = 2 \frac{q^n(1-q^n)}{ 1-q^{2n}} + \...

### Old Math Books Request

Two classic and influential ones on abstract algebra which are still missing in the other answers: Heinrich Weber: Lehrbuch der Algebra. Vol. 1 (1895), Vol. 2 (1895), Vol. 3 (1898) Bartel van der ...
Accepted

### Origin of quote “In order to simplify…”

I'm going to deviate from my usual policy of never answering a question because I can't "really" post images in comments, and complex google searches may yield different results for ...

### Are there cases where a flawed proof seems correct?

It does seem to happen on a regular basis that a physics-y argument is given that purports to prove the Riemann Hypothesis... but, also, at the same time would seem to prove some other things which we ...
A number of results in analysis were proven then counterexamples were later found. For example Ampere proved in 1806 that any continuous function from $\mathbb{R}$ to itself is differentiable ...