# Gelfond-Schneider constant

The Gelfond-Schneider constant^{} ${2}^{\sqrt{2}}$ was one of the first numbers to be proven to be transcendental by appying Gelfond’s theorem. However, naming the constant after Gelfond and Schneider comes from Eric Weisstein, with many people preferring to refer to it simply as 2 to the power of square root of 2^{}.

Its value in base 10 is approximately 2.66514414269022518865029724987313984827421131371. Its continued fraction^{} representation is neither terminating nor periodic, and begins

$$2+\frac{1}{1+\frac{1}{1+\frac{1}{1+\frac{1}{72+\mathrm{\cdots}}}}}$$ |

Title | Gelfond-Schneider constant |
---|---|

Canonical name | GelfondSchneiderConstant |

Date of creation | 2013-03-22 18:54:36 |

Last modified on | 2013-03-22 18:54:36 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11J81 |