{"product_id":"borels-methods-of-summability","title":"Borel's Methods of Summability","description":"\u003cp\u003eSummability methods are transformations that map sequences (or functions) to sequences (or functions).  A prime requirement for a \"good\" summability method is that it preserves convergence.  Unless it is the identity transformation, it will do more: it will transform some divergent sequences to convergent sequences.  An important type of theorem is called a Tauberian theorem. Here, we know that a sequence is summable.  The sequence satisfies a\n\u003cbr\u003efurther property that implies convergence.  Borel's methods are fundamental to a whole class of sequences to function methods.  The transformation gives a function that is usually\n\u003cbr\u003eanalytic in a large part of the complex plane, leading to a method for analytic continuation.  These methods, dated from the beginning of the 20th century, have recently found applications in some problems in theoretical physics.\u003c\/p\u003e","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":46058431709422,"sku":"9780198535850","price":172.82,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0630\/9612\/7726\/files\/9780198535850.jpg?v=1736475625","url":"https:\/\/bookland.com.au\/products\/borels-methods-of-summability","provider":"Book Land AU","version":"1.0","type":"link"}