OEIS/Eta products

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Revision as of 14:28, 23 January 2023 by imported>Gfis (Created page with "===Dedekind eta η=== * [https:oeis.org/A000700 A000700] ===Jacobi theta_2 === ===Jacobi θ_3, Ramanujan phi φ === [https://oeis.org/A000122 A000122] 1, 2, 0, 0,...")
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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.