{"product_id":"borel-s-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 further 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 analytic 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":"Bruce L. R. Shawyer","offers":[{"title":"Default Title","offer_id":43575277649981,"sku":"9780198535850","price":213.0,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0597\/7689\/2989\/files\/9780198535850.jpg?v=1788562108","url":"https:\/\/www.palmleaf.com.au\/products\/borel-s-methods-of-summability","provider":"Palmleaf","version":"1.0","type":"link"}