A distinctive Sumudu treatment of trigonometric functions

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• 作者：Fethi Bin Muhammad Belgacem^a ; ^{fbmbelgacem@gmail.com" class="auth_mail" title="E-mail the corresponding author} ; Rathinavel Silambarasan^b ; ^{silambu_vel@yahoo.co.in" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Sumudu transform ; Laplace transform ; Trigonometric functions
• 刊名：Journal of Computational and Applied Mathematics
• 出版年：2017
• 出版时间：1 March 2017
• 年：2017
• 卷：312
• 期：Complete
• 页码：74-81
• 全文大小：460 K

文摘

The Sumudu transform integral equation is solved by continuous integration by parts, to obtain its definition for trigonometric functions. The transform variable, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716000029&_mathId=si153.gif&_user=111111111&_pii=S0377042716000029&_rdoc=1&_issn=03770427&md5=55c30a43f2e1205603cfe0ca7d020bb9" title="Click to view the MathML source">uclass="mathContainer hidden">class="mathCode">, is included as a factor in the argument of class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0377042716000029&_mathId=si9.gif&_user=111111111&_pii=S0377042716000029&_rdoc=1&_issn=03770427&md5=25f65b3ce7ba2360efa03bfedaeaf698" title="Click to view the MathML source">f(t)class="mathContainer hidden">class="mathCode">, and summing the integrated coefficients evaluated at zero yields the image of trigonometric functions. The obtained result is inverted to show the expansion of trigonometric functions as an infinite series. Maple graphs, tables of extended Sumudu properties, and infinite series expansions of trigonometric functions Sumudi images are given.