{"product_id":"elegant-techniques-for-zeta-and-edgar-gzeto-9788409841486","title":"Elegant Techniques for Zeta and Harmonic Series: A new accessible approach to the Basel problem, Euler sums, and Plouffe identities","description":"\u003cp\u003e\u003cb\u003eRediscover Zeta and Harmonic Series Through a Bold New Algebraic Perspective\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eThe Basel Problem was famously solved by \u003cb\u003eEuler\u003c\/b\u003e, who unveiled the beauty of even zeta values and odd beta values. Since then, the landscape of infinite series has expanded through the work of many great mathematicians like \u003cb\u003eDirichlet, Ramanujan, \u003c\/b\u003eor\u003cb\u003e Zagier\u003c\/b\u003e, among many others-often requiring advanced and heavy machinery.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eWhat if there was a simpler way?\u003c\/b\u003e\u003c\/p\u003e\u003cp\u003eThis book introduces a compelling alternative technique that naturally unifies these famous results. By focusing on the algebraic interrelations between quantities, this method sheds new light on the links between \u003cb\u003eparticular integer zeta values\u003c\/b\u003e, \u003cb\u003eEuler sums\u003c\/b\u003e, and \u003cb\u003ePlouffe identities\u003c\/b\u003e.\u003c\/p\u003e\u003cp\u003e\u003cb\u003eThe best part?\u003c\/b\u003e You'll find yourself absorbed while exploring the different paths each chapter opens.\u003c\/p\u003e\u003cp\u003eWhether you are a student or a seasoned researcher, this book provides a fresh toolkit for evaluating series and leaves you with open questions ready to be taken to the next frontier of mathematical discovery.\u003cbr\u003e \u003c\/p\u003e\u003cb\u003eWhat's Inside this book\u003c\/b\u003e\u003cul\u003e\n\u003cli\u003e\n\u003cb\u003eIntroduction\u003c\/b\u003e: we cover the motivation for the problem of evaluating the zeta function at 2, 3, 4, 5, ...\u003c\/li\u003e\n\u003cli\u003eCh2 - \u003cb\u003eSolving the Basel problem\u003c\/b\u003e: we introduce the new technique, develop the relations between all zeta(2n), and then solve the Basel challenge.\u003c\/li\u003e\n\u003cli\u003eCh3 - \u003cb\u003eBasic harmonic series\u003c\/b\u003e: we find all the simple Euler sums of harmonic numbers and the skew harmonic version, over all powers of natural and odd numbers. We also cover alternating sums and series with odd-based harmonics, with partial results.\u003c\/li\u003e\n\u003cli\u003eCh4 - \u003cb\u003eHigher order harmonic series\u003c\/b\u003e: we extend the results to series that contain higher order harmonics over natural and odd denominators. We cover how the technique covers some powers and products, and a few generalizations.\u003c\/li\u003e\n\u003cli\u003eCh5 - \u003cb\u003eQuadratics and pure zeta-family identities\u003c\/b\u003e: we go back to the initial quadratic identity developed at chapter 2, do a deeper exploration and expand and find other quadratic identities. We cover the odd-integer betas, and end up considering all products between the zeta family values and do some other explorations.\u003c\/li\u003e\n\u003cli\u003eCh6 - \u003cb\u003eFourth degree series\u003c\/b\u003e: the shape of the functions suggest this next exploration, where we find the connection with hyperbolic cotangent. There's room to still get alternative pure-zeta identities, others containing harmonics and more.\u003c\/li\u003e\n\u003cli\u003eCh7 - \u003cb\u003ePlouffe-Ramanujan identities\u003c\/b\u003e: using the results from previous chapter we prove many of Plouffe's identities and generalize some related Ramanujan identities, covering not only odd-argument zetas but also even-argument betas.\u003c\/li\u003e\n\u003cli\u003eCh8 - \u003cb\u003eDigamma explorations\u003c\/b\u003e: in this chapter we unify previous results and find further examples of these zeta series representations. We also find quadratic closed forms free of harmonics and other artifacts.\u003c\/li\u003e\n\u003cli\u003eCh9 - \u003cb\u003eHigher degree series\u003c\/b\u003e: we retake exploration of cubics, sixties and 8th degree identities.\u003c\/li\u003e\n\u003cli\u003eCh10 - \u003cb\u003eExploring series with factorials\u003c\/b\u003e: we generalize some key concepts from Chapter 2 and apply to series based on factorials, developing new and surprising identities. In this chapter we use integration techniques a few times.\u003c\/li\u003e\n\u003cli\u003eCh11 - \u003cb\u003eInspiring infinite product\u003c\/b\u003e: following Euler's ideas, we develop generic series identities that allow us to obtain general higher-order harmonic sums, complementing previous chapters' results.\u003c\/li\u003e\n\u003cli\u003eAppendix A\u003cb\u003e \u003c\/b\u003e- \u003cb\u003eA special limit\u003c\/b\u003e: we look into more detail to a limit that acts as general example needed to obtain some results.\u003c\/li\u003e\n\u003cli\u003eAppendix B - \u003cb\u003eSums tables\u003c\/b\u003e: summary of a certain type of sums tabulated for low degrees, along with methods to obtain them.\u003c\/li\u003e\n\u003c\/ul\u003e\u003cbr\u003e\u003cbr\u003e\u003cb\u003eAuthor:\u003c\/b\u003e Edgar Güeto\u003cbr\u003e\u003cb\u003eISBN-10:\u003c\/b\u003e 8409841487\u003cbr\u003e\u003cb\u003eISBN-13:\u003c\/b\u003e 9788409841486\u003cbr\u003e\u003cb\u003ePublisher:\u003c\/b\u003e Edgar Gueto de la Rosa\u003cbr\u003e\u003cb\u003eLanguage:\u003c\/b\u003e English\u003cbr\u003e\u003cb\u003ePublished:\u003c\/b\u003e 05\/26\/2026\u003cbr\u003e\u003cb\u003ePages:\u003c\/b\u003e 384\u003cbr\u003e\u003cb\u003eFormat:\u003c\/b\u003e Paperback\u003cbr\u003e\u003cb\u003eWeight:\u003c\/b\u003e 1.13lbs\u003cbr\u003e\u003cb\u003eSize:\u003c\/b\u003e 9.00h x 6.00w x 0.79d","brand":"Edgar Güeto","offers":[{"title":"Paperback","offer_id":49001900966143,"sku":"9788409841486","price":30.88,"currency_code":"USD","in_stock":true}],"url":"https:\/\/www.whiterainbookhouse.com\/products\/elegant-techniques-for-zeta-and-edgar-gzeto-9788409841486","provider":"WR Book House","version":"1.0","type":"link"}