{"product_id":"9789814449632","title":"Contributions To The Theory Of Zeta-functions: The Modular Relation Supremacy: The Modular Relation Supremacy","description":"\u003cp\u003eThis volume provides a systematic survey of almost all the equivalent assertions to the functional equations — zeta symmetry — which zeta-functions satisfy, thus streamlining previously published results on zeta-functions. The equivalent relations are given in the form of modular relations in Fox \u003ci\u003eH\u003c\/i\u003e-function series, which at present include all that have been considered as candidates for ingredients of a series. The results are presented in a clear and simple manner for readers to readily apply without much knowledge of zeta-functions.\u003c\/p\u003e\u003cp\u003eThis volume aims to keep a record of the 150-year-old heritage starting from Riemann on zeta-functions, which are ubiquitous in all mathematical sciences, wherever there is a notion of the norm. It provides almost all possible equivalent relations to the zeta-functions without requiring a reader's deep knowledge on their definitions. This can be an ideal reference book for those studying zeta-functions.\u003c\/p\u003e\u003cb\u003eContents:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003ePrelude\u003c\/li\u003e\n\u003cli\u003eGrocery of Special Functions\u003c\/li\u003e\n\u003cli\u003eUnprocessed Modular Relations\u003c\/li\u003e\n\u003cli\u003eFourier-Bessel Expansion \u003ci\u003eH\u003c\/i\u003e\u003csup\u003e1;1\u003c\/sup\u003e\u003csub\u003e1;1\u003c\/sub\u003e↔ \u003ci\u003eH\u003c\/i\u003e\u003csup\u003e2;0\u003c\/sup\u003e\u003csub\u003e0;2\u003c\/sub\u003e\n\u003c\/li\u003e\n\u003cli\u003eThe Ewald Expansion or the Incomplete Gamma Series\u003c\/li\u003e\n\u003cli\u003eThe Riesz Sums\u003c\/li\u003e\n\u003cli\u003eThe General Modular Relation\u003c\/li\u003e\n\u003cli\u003eThe Hecke Type Zeta-functions\u003c\/li\u003e\n\u003cli\u003eThe Product of Zeta-functions\u003c\/li\u003e\n\u003cli\u003eMiscellany\u003c\/li\u003e\n\u003cbr\u003e\n\u003c\/ul\u003e\u003cb\u003eReadership:\u003c\/b\u003e Graduate students and researchers in functional equations and special functions.\u003cbr\u003e\u003cb\u003eKey Features:\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003eThe book gives a thorough description of a.a. possible equivalent relations to the functional equation in terms of the \u003ci\u003eH\u003c\/i\u003e-function series for zeta-functions that have been studied\u003c\/li\u003e\n\u003cli\u003eGiven a functional equation, the book immediately informs the reader of the direction to be taken to reach the ultimate aim concerning the zeta-function in both pure and applied disciplines\u003c\/li\u003e\n\u003cli\u003eThe reader can forget about the difficult definition of zeta-functions themselves and can refer to the form of functional equation and check how multiple is the gamma factor\u003c\/li\u003e\n\u003c\/ul\u003e","brand":"World Scientific Publishing Company, Incorporated","offers":[{"title":"Default Title","offer_id":47144689631472,"sku":"9789814449632","price":46.0,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0737\/7593\/9824\/files\/9789814449632_p0.jpg?v=1763691030","url":"https:\/\/shop-qa.barnesandnoble.com\/products\/9789814449632","provider":"Barnes \u0026 Noble (DEV)","version":"1.0","type":"link"}