# Gelfond’s constant

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

Its value in base 10 is approximately 23.1406926327792690057290863679485473802661062426. Its continued fraction^{} representation is neither terminating nor periodic, and begins

$$23+\frac{1}{7+\frac{1}{9+\frac{1}{3+\mathrm{\cdots}}}}$$ |

Title | Gelfond’s constant |
---|---|

Canonical name | GelfondsConstant |

Date of creation | 2013-03-22 18:54:34 |

Last modified on | 2013-03-22 18:54:34 |

Owner | PrimeFan (13766) |

Last modified by | PrimeFan (13766) |

Numerical id | 4 |

Author | PrimeFan (13766) |

Entry type | Definition |

Classification | msc 11J81 |