Transcendental Number - Numbers Which May or May Not Be Transcendental

Numbers Which May or May Not Be Transcendental

Numbers which have neither been proven algebraic nor proven transcendental:

  • Sums, products, powers, etc. of the number π and the number e, except for eπ (Gelfond's constant), which is known to be transcendental: π + e, π − e, π·e, π/e, ππ, ee, πe.
  • The Euler–Mascheroni constant γ (which has not been proven to be irrational).
  • Catalan's constant, also not known to be irrational.
  • Apéry's constant, ζ(3) (which Apéry proved is irrational)
  • The Riemann zeta function at other odd integers, ζ(5), ζ(7), ... (not known to be irrational.)
  • The Feigenbaum constants, and .

Conjectures:

  • Schanuel's conjecture,
  • Four exponentials conjecture.

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