Consider that since , and therefore, somewhat unexpectly:

we can use it to construct new identities thusly

Let

Let

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])

>>>

>>> A

mpf(‘1.9109509100512501’)

>>> B = fp.nprod(lambda m: (1+1/(m**3))**(1/exp(m)), [1,inf])

>>>

>>> B

mpf(‘1.3140291251423164’)

>>> A**log(B)

mpf(‘1.1934623097049237’)

>>> B**log(A)

mpf(‘1.1934623097049237’)