# ^3 square root x

Input |
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x^(1/3) |

Root |

x = 0 |

Derivative |

d/dx(x^(1/3)) = 1/(3 x^(2/3)) |

Indefinite integral |

integral x^(1/3) dx = (3 x^(4/3))/4 + constant |

Global minimum |

min{x^(1/3)} = 0 at x = 0 |

Series representation |

x^(1/3) = sum_(n=0)^infinity binomial(1/3, n) (-1 + x)^n for abs(1 – x)<1 |

Integral representation |

(1 + z)^a = ( integral_(-i infinity + gamma)^(i infinity + gamma) (Gamma(s) Gamma(-a – s))/z^s ds)/((2 pi i) Gamma(-a)) for (0 |