Dedekind eta η
- [https:oeis.org/A000700 A000700]
Jacobi theta_2
Jacobi θ_3, Ramanujan phi φ
A000122 1, 2, 0, 0, 2, 0, 0, 0, 0, 2, 0, 0, 0, 0, 0, 0, 2
eta(q^2)^5 / (eta(q)*eta(q^4))^2
Euler transform of period 4: [2,-3,2,-1]
eps P="[2,5;1,-2;4,-2]"
Jacobi θ_4
A002448 1, -2, 0, 0, 2, 0, 0, 0, 0, -2, 0, 0, 0, 0, 0, 0, 2
eta(q)^2 / eta(q^2)
Euler transform of period 2: [2,-1]
eps P="[1,2;2,-1]"
Ramanujan psi ψ
- [https:oeis.org/A000700 A000700]
Ramanujan chi χ
- [https:oeis.org/A000700 A000700]
Ramanujan f
Cookbook
- For all tuples [m,k] add m*k.
- The resulting integer part gives the q-shift, while the fractional part is noted before the eta product.