Accession Number:

AD0600444

Title:

CERTAIN SUMMATIONS INVOLVING BINOMIAL COEFFICIENTS AND THEIR RELATION TO DYSON'S CONJECTURE.

Descriptive Note:

Corporate Author:

HARRY DIAMOND LABS WASHINGTON D C

Personal Author(s):

• Karayianis,N.

Report Date:

1964-04-20

Pagination or Media Count:

18.0

Abstract:

This report concerns itself with a theorem, a mathematical trick, and a conjecture which resulted from the study of a previous conjecture by F. J. Dyson. The theorem regards a certain summation over binomial coefficients. A special case of this theorem is then used in conjunction with a mathematical trick to prove a special case of Dysons conjecture. Finally, a conjecture is proposed that is a modest generalization of Dysons conjecture in the sense that the latter follows very simply. Some evidence in support of the conjecture is presented however its validity remains an open question. Author

Descriptors:

• *BINOMIALS
• THEOREMS
• POWER SERIES
• SERIES(MATHEMATICS)
• FUNCTIONS(MATHEMATICS)
• NUMBER THEORY
• STATISTICAL ANALYSIS

Subject Categories:

Distribution Statement:

APPROVED FOR PUBLIC RELEASE