Erdosian functions and an identity of gauss

dc.contributor.author	Chatterjee, T.
dc.contributor.author	Khurana, S.S.
dc.date.accessioned	2020-01-03T11:36:17Z
dc.date.available	2020-01-03T11:36:17Z
dc.date.issued	2020-01-03
dc.identifier.uri	http://localhost:8080/xmlui/handle/123456789/1468
dc.description.abstract	A famous identity of Gauss gives a closed form expression for the values of the digamma function ðxÞ at rational arguments x in terms of elementary functions. Linear combinations of such values are intimately connected with a conjecture of Erd}os which asserts non vanishing of an infinite series associated to a certain class of periodic arithmetic functions. In this note we give a different proof for the identity of Gauss using an orthogonality like relation satisfied by these functions. As a by product we are able to give a new interpretation for nth Catalan number in terms of these functions.	en_US
dc.language.iso	en_US	en_US
dc.subject	Dirichlet series	en_US
dc.subject	Erd}os conjecture	en_US
dc.subject	Gauss identity	en_US
dc.subject	Digamma function.	en_US
dc.title	Erdosian functions and an identity of gauss	en_US
dc.type	Article	en_US