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It targets readers already familiar with calculus, including improper integrals, and develops core properties using elementary calculus methods. The work explicitly notes omissions such as extensions to complex variables, Hölder’s theorem, Kummer’s series, and specific derivative-related formulas, while explaining that the theory is built from an integral definition and log-convexity techniques. ",{"@graph":69,"@context":121},[70,84,104],{"@type":71,"itemListElement":72},"BreadcrumbList",[73,77,79,82],{"item":74,"name":75,"@type":76,"position":8},"https://docshare.wps.com","Home","ListItem",{"item":78,"name":9,"@type":76,"position":14},"https://docshare.wps.com/document/",{"item":80,"name":15,"@type":76,"position":81},"https://docshare.wps.com/document/literature/",3,{"item":83,"name":65,"@type":76,"position":19},"https://docshare.wps.com/document/the-gamma-function-editors-preface-artin-monograph/440897/",{"url":83,"name":65,"@type":85,"image":86,"author":91,"headline":65,"publisher":94,"fileFormat":97,"inLanguage":63,"description":67,"dateModified":98,"datePublished":98,"encodingFormat":97,"isAccessibleForFree":99,"interactionStatistic":100},"DigitalDocument",{"url":87,"@type":88,"width":89,"height":90},"https://docshare.wps.com/thumbnails/the-gamma-function-editors-preface-artin-monograph/440897.png","ImageObject",300,407,{"name":92,"@type":93},"Mia  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discuss extensions to complex variables, Hölder’s theorem about no algebraic differential equation, Kummer’s series and an integral representation for log I(x), and formulas for the logarithmic derivative of T(x).","https://schema.org",{"og:url":83,"og:type":123,"og:title":65,"og:site_name":95,"og:description":67},"article",{"robots":125,"canonical":83},"index,follow",{"doc_id":127,"site_id":62},440897,1790693838,{"code":4,"msg":5,"data":130},{"doc_id":127,"user_id":131,"nickname":92,"user_avatar":132,"doc_module":4,"category_id":14,"category_name":15,"doc_title":65,"doc_description":67,"doc_content":133,"file_id":134,"file_url":135,"file_type":136,"file_size":137,"view_count":4,"is_deleted":4,"is_public":8,"is_downloadable":8,"audit_status":8,"page_count":138,"language":139,"language_code":63,"site_id":62,"html_lang":63,"table_of_contents":140,"faqs":141,"seo_title":142,"seo_description":67,"update_tm":128,"read_time":143},687207024478,"https://ap-avatar.wpscdn.com/davatar_a8503ba1806abce46bf441b54a3ca4cd","# The Gamma Function\n\n4.Covder  \nhttps://archive.org/details/gammafunction0000unse  \n## The Gamma Function\n\n## Athena\n\nSeries  \nSELECTED TOPICS IN MATHEMATICS  \nEdwin Hewitt,Editor  \nAMBROSE,LAZEROWITZ:  LoGIC:THE THEORY OF FoRMAL INFERENCE  \nARTIN:  THE GAMMA FUNCTION.TRANSLATED BY MICHAEL BUTLER  \nBELLMAN:  \nA BRIEF INTRODUCTION TO THETA FUNCTIONS  \nBELLMAN:PERTURBATION TECHNIQUES IN MATHEMATICS,PHYSICS,AND ENGINEERING  \n  THE BoOK ON GAMES OF CHANCE  \nCARDANO:  \nERDÉLYI:  \nOPERATIONAL CALCULUS AND GENERALIZED FUNCTIONS  \nFICKEN:  \nTHE SIMPLEX METHOD OF LINEAR PROGRAMMING  \nHADWIGER,DEBRUNNER,AND KLEE::  CoMBINATORIAL GEOMETRYIN THE PLANE  \nHEINS:SELECTED TOPICS IN THE CLASSICAL THEORY OF FUNCTIONSOF A COMPLEX VARIABLE  \nHIRSCHMAN:  INFINITE SERIES  \nHOCHSTADT:  SPECIAL FUNCTIONS OF MATHEMATICAL PHYSICS  \nJANS:  RINGS AND HOMOLOGY  \nKAZARINOFF:  ANALYTIC INEQUALITIES  \nWILLIAMSON:  LEBESGUE INTEGRATION  \nTranslated by  \nMichael Butler  \n## The Gamma Function\n\nEmil Artin  \nProfessor of MathematicsHamburg University  \nHOLT,RINEHART AND WINSTON  \nNew York ·Chicago ·San FranciscoToronto ·London  \nThe German original,  \n\"Einführung in die Theorie der Gammafunktion,\"  \nappeared in the  \nHamburger Mathematische Einzelschriften  \n1.Heft/1931,published by Verlag B.G.Teubner,Leipzig  \nEnglish TranslationCopyright C1964 by  \nHolt,Rinehart and Winston,Inc.  \nLibrary of Congress Catalog Card Number:64-2299420526-0114  \nPrinted in the United States of AmericaAll Rights Reserved  \n## Editor's Preface\n\nA generation has passed since the late Emil Artin's little classic on thegamma function appeared in the Hamburger Mathematische Einzelschriften.Since that time,it has been read with joy and fascination by many thousandsof mathematicians and students of mathematics.In the United States(andpresumably elsewhere as well),it has for many years been hard to find,anddog-eared copies and crude photocopies have been passed from hand to hand.Professor Artin's monograph has given many a student his first look at genuineanalysis—the delicacy of its arguments,the precision of its results.Artin hada deep feeling for these aspects of analysis,and he treated them with a master'shand.His undergraduate lectures in the calculus,for example,were filled withelegant constructions and theorems which,alas,Artin never had time to putinto printed form.We may be all the more grateful for this beautiful essay,and for its appearance in a new English edition.Various changes made byArtin himself have been incorporated in the present edition.In particular asmall error following formula (59)(this edition)was corrected on the basis ofa suggestion by Professor Borge Jessen.  \nFinally,thanks are due to the translator,Mr.Michael Butler,and to thefirm of B.G.Teubner for English-language rights.  \nEDWIN HEWITT  \nSeattle,WashingtonMay,1964  \n## Preface\n\nI have written this monograph with the hope of filling in a certain gapwhich has often been felt to exist in the mathematical literature.Despite theimportance of the gamma function in many different parts of mathematics,calculus books often treat this function in a very sketchy and complicatedfashion.I feel that this monograph will help to show that the gamma functioncan be thought of as one of the elementary functions,and that all of its basicproperties can be established using elementary methods of the calculus.  \nAs far as prerequisites are concerned,the reader need only be well acquainted,with calculus,including improper integrals.Some of the more importantconcepts needed will even be introduced and discussed again in the first chapter.With this background the reader should have no trouble understanding every-thing but the later parts of the last two chapters,which do assume some knowl-edge of Fourier series.But then,these parts of the monograph can be passedover on a first reading without any difficulty whatsoever.  \nThe following parts of the theory will not be discussed:  \n(1)Extension to complex variables.For those familiar ","cbCaids6KlrolEXs","https://ap.wps.com/l/cbCaids6KlrolEXs","pdf",2883728,56,"English","# Editor's Preface\n## Preface","[{\"question\":\"What does the monograph aim to address about the gamma function in the literature?\",\"answer\":\"It aims to fill a gap where calculus books often treat the gamma function too sketchily and in an overly complicated fashion.\"},{\"question\":\"What prerequisites does the author require from the reader?\",\"answer\":\"The reader needs to be well acquainted with calculus, including improper integrals, and some later parts assume knowledge of Fourier series.\"},{\"question\":\"Which topics are explicitly not discussed in the monograph?\",\"answer\":\"It does not discuss extensions to complex variables, Hölder’s theorem about no algebraic differential equation, Kummer’s series and an integral representation for log I(x), and formulas for the logarithmic derivative of T(x).\"}]","The Gamma Function - Editor's Preface - Artin Monograph | PDF",86]