On the Evaluation of the Integral $$int_0^{{pi mathord{left/ {vphantom {pi 4}} right. kern-nulldelimiterspace} 4}} {ln left( {cos ^{{m mathord{left/ {vphantom {m n}} right. kern-nulldelimiterspace} n}} theta pm sin ^{{m mathord{left/ {vphantom {m n}} right. kern-nulldelimiterspace} n}} theta } right)dtheta } $$期刊界 All Journals 搜尽天下杂志传播学术成果专业期刊搜索期刊信息化学术搜索

On the Evaluation of the Integral $$int_0^{{pi mathord{left/ {vphantom {pi 4}} right. kern-nulldelimiterspace} 4}} {ln left( {cos ^{{m mathord{left/ {vphantom {m n}} right. kern-nulldelimiterspace} n}} theta pm sin ^{{m mathord{left/ {vphantom {m n}} right. kern-nulldelimiterspace} n}} theta } right)dtheta } $$

Authors:	Zucker I.J. Joyce G.S. Delves R.T.

Affiliation:	1. Wheatstone Physics Laboratory, King's College, University of London, Strand, London, WC2R 2LS, U.K.

Abstract:	The integral $$int_0^{{pi mathord{left/ {vphantom {pi 4}} right. kern-nulldelimiterspace} 4}} {ln left( {cos ^{{m mathord{left/ {vphantom {m n}} right. kern-nulldelimiterspace} n}} theta pm sin ^{{m mathord{left/ {vphantom {m n}} right. kern-nulldelimiterspace} n}} theta } right)dtheta } $$ where m and n are relatively prime positive integers, is evaluated exactly in terms of elementary functions and the Catalan constant G.

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