| 释义 |
Carlson-Levin ConstantN.B. A detailed on-line essay by S. Finchwas the starting point for this entry.
Assume that  is a Nonnegative Real function on  and that the twointegrals
 | (1) |
 | (2) |
 and  , Carlson (1934) determined
 | (3) |
 is the best constant (in the sense that counterexamples can be constructed for any stricter Inequality which uses a smaller constant). For the general case
 | (4) |
 | (5) |
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.
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