Consider that since , and therefore, somewhat unexpectly:
we can use it to construct new identities thusly
Therefore, since we know that we can use that
to explicitly calculate a new identity thusly:
1. Compute the logarithm of , :
2. Compute the logarithm of , :
3. Combine them:
>>> A = fp.nprod(lambda n: sqrt(1+1/(n*n)), [1,inf])
>>> B = fp.nprod(lambda m: (1+1/(m**3))**(1/exp(m)), [1,inf])
one: It is a thick, yellow, Springer-Verlag dealie, illustrated and about fractals. There is a color plate on nearly every page. I dreamt of being in a bookshop and considering buying it.
two: has lots of equations at the beginning, and they change as I read them. last page has a distorting/metamorphosing picture of einstein/feynman in green and blue hues.
three: also a text that changes, I remember a diagram of helix against a point scatter. Also changed.
last night: I remember something about the Euler-Mascheroni constant . Impenetrable references section. Also picture of fractals.
Have you dreamt of reading mathematics books? If so, leave a comment about them.
here is the source, compile with
gcc syllegy.c -o syllegy -lm
Here’s a puzzle: consider that the Gamma function is the interpolation of the factorials. What about interpolating the primorials. If is the $n$-th prime, then what is the correct analogue of the Gamma function if we define the primorial as:
This is something I’m working on: