Hi everyone, I'm the creator of this! Thanks for posting this, I tried to post it once and it just didn't take off so I wasn't sure if I should post again. I'll read all the feedback now.
Cool! I've just contributed several examples. If anyone is interested in the sheer amount of identities that have been discovered, good books are (many of them gigantic references spanning thousands of pages). When bored, try proving some of those facts, examples build on top of each other. These are not the only examples, as there are
many texts like these in other areas of mathematics and engineering, be it numerical analysis, optimization and variational analysis, statistics, abstract algebra, control theory, geometry and so on.
Table of Integrals, Series, and Products, Gradshteyn & Ryzhik.
Special Integrals of Gradshteyn and Ryzhik, Vols. I and II, Moll for some proofs of the above.
Handbook of Integral Equations, Polyanin & Manzhirov.
Scalar, Vector, and Matrix Mathematics, Bernstein.
Handbook of Number Theory I and II, Sandor, Crstici & Mitrinovic.
Wikipedia also has a plethora of pages with mathematical identities. Some of them:
Can't have a list like that without a mention of Abramowitz & Stegun [0], or its successor, the NIST Digital Library of Mathematical Functions [1]. It's about as comprehensive as it gets.
Those formulas with i as interest rates are really tripping me up. I mean (1+i)^n just looks like it aught to be complex.
Edit: I'm also not too happy with the explanation of Feymann's trick, it fails to properly explain Feynman's trick, says n! is the gamma function, and applies the trick to an integral which follows directly from the definition of the Gamma function and cannot be simplified without that definition.
Hi, creator here. Thanks for the feedback, I've been kind of using this site just to store things that I find personally useful and in ways that I, an undergraduate student, understand so I'm sure there are some corners being cut like in the case of Feynman's trick. Do you think you could help me improve that page? The source code is here: https://github.com/stemformulas/stemformulas.github.io/blob/...
I'd remove that page entirely, perhaps in favour of one that simply lists the definition of the Gamma function (which is basically the formula there right now).
You can't summarize Feynman's trick in one formula. At best you can list an example, and I'd argue this isn't the best one.
I think this is great, though still only about 80% there.
Some helpful additions would be labeling which values are constants, examples of both how and where the equation is used, and numerical representations of the formulae.
When I click on Schrodinger's eq I want to be able to click on the Wave function and see an example of the numerical form, ie a matrix of vectors with toy values.
When I started out, I added examples to formulas, but it did require a lot more effort per formula and as I am adding these formulas on my own (contributors please!) I chose to prioritize quantity first. The rest of your suggestions are good, I'll add them to my list of ideas, thank you.
Yeah, it's gonna be a while until I can have a lot of formulas, but I do think I'm adding value in a few ways:
- Copying LaTeX on formula pages
- Formulas have an open-graph preview so if they are linked on social media you can see the formulas in the preview
- The search is the main page, in focus, so you can realistically open a new browser tab and find a formula that you know exists in under a second.
- Hidden feature: the forward-slash (/) key also triggers the search dialogue, so minimal mouse is needed ever while navigating the site.
I built this because of my frustration with Wikipedia actually. A lot of Wikipedia pages are really rigorous, but when I visit I just want to know the common form of the main equation, which is sometimes placed a few headings down.
Lean mathlib may already have the proofs for many of these Stem Formulas (in LaTeX)? These formulas as SymPy would also be useful.
latex2sympy parses LaTeX and generates SymPy symbolic CAS Python code (w/ ANTLR) and is now merged in SymPy core but you must install ANTLR before because it's an optional dependency. Then, sympy.lambdify will compile a symbolic expression for use with TODO JAX, TensorFlow, PyTorch,.
>> """Convert a SymPy expression into a function that allows for fast numeric evaluation [with the CPython math module, mpmath, NumPy, SciPy, CuPy, JAX, TensorFlow, SymPy, numexpr,]*
