Values of the derivatives of the cotangent at rational multiples of π

✍ Scribed by Djurdje Cvijović

• Book ID: 104000521
• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 359 KB
• Volume: 22
• Category: Article
• ISSN: 0893-9659
• DOI: 10.1016/j.aml.2008.03.013

✦ Synopsis

a b s t r a c t By elementary arguments, we deduce closed-form expressions for the values of all derivatives of the cotangent function at rational multiples of π. These formulae are considerably simpler than similar ones which were found in a different manner by Kölbig. Also, we show that the values of cot (n)

6 and 5 6 are expressible in terms of the values of the Bernoulli polynomials alone.