Koshliakov kernel and identities involving the Riemann zeta function

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• 作者：Atul Dixit^a ; ^{adixit@tulane.edu" class="auth_mail" title="E-mail the corresponding author} ; Nicolas Robles^b ; ^{nicolas.robles@math.uzh.ch" class="auth_mail" title="E-mail the corresponding author} ; Arindam Roy^c ; ^{roy22@illinois.edu" class="auth_mail" title="E-mail the corresponding author} ; Alexandru Zaharescu^c ; ^d ; ^{zaharesc@illinois.edu" class="auth_mail" title="E-mail the corresponding author}
• 关键词：Riemann zeta function ; Hurwitz zeta function ; Bessel functions ; Koshliakov
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2016
• 出版时间：15 March 2016
• 年：2016
• 卷：435
• 期：2
• 页码：1107-1128
• 全文大小：515 K

文摘

Some integral identities involving the Riemann zeta function and functions reciprocal in a kernel involving the Bessel functions class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1501032X&_mathId=si1.gif&_user=111111111&_pii=S0022247X1501032X&_rdoc=1&_issn=0022247X&md5=85c859261ded0d23bce164108381fc36" title="Click to view the MathML source">J_z(x)class="mathContainer hidden">class="mathCode">$J_z(x)$, class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1501032X&_mathId=si2.gif&_user=111111111&_pii=S0022247X1501032X&_rdoc=1&_issn=0022247X&md5=5d2d3104d287f5b2cbce651b27e5d167" title="Click to view the MathML source">Y_z(x)class="mathContainer hidden">class="mathCode">$Y_z(x)$ and class="mathmlsrc">class="formulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0022247X1501032X&_mathId=si3.gif&_user=111111111&_pii=S0022247X1501032X&_rdoc=1&_issn=0022247X&md5=381c3c03cb93b6cb1774b930d4949d63" title="Click to view the MathML source">K_z(x)class="mathContainer hidden">class="mathCode">$K_z(x)$ are studied. Interesting special cases of these identities are derived, one of which is connected to a well-known transformation due to Ramanujan, and Guinand.