*N.B. A detailed on-line essay by S. Finch
was the starting point for this entry.*

Assume that is a Nonnegative Real function on and that the two
integrals

(1) |

(2) |

(3) |

(4) |

(5) |

(6) | |||

(7) | |||

(8) |

and is the Gamma Function.

**References**

Beckenbach, E. F.; and Bellman, R. *Inequalities.* New York: Springer-Verlag, 1983.

Boas, R. P. Jr. Review of Levin, V. I. ``Exact Constants in Inequalities of the Carlson Type.'' *Math. Rev.* **9**, 415, 1948.

Finch, S. ``Favorite Mathematical Constants.'' http://www.mathsoft.com/asolve/constant/crlslvn/crlslvn.html

Levin, V. I. ``Exact Constants in Inequalities of the Carlson Type.'' *Doklady Akad. Nauk. SSSR (N. S.)*
**59**, 635-638, 1948. English review in Boas (1948).

Mitrinovic, D. S.; Pecaric, J. E.; and Fink, A. M. *Inequalities Involving Functions and Their
Integrals and Derivatives.* Kluwer, 1991.

© 1996-9

1999-05-26