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The Resource The Rise and Development of the Theory of Series up to the Early 1820s, by Giovanni Ferraro, (electronic resource)
The Rise and Development of the Theory of Series up to the Early 1820s, by Giovanni Ferraro, (electronic resource)
Resource Information
The item The Rise and Development of the Theory of Series up to the Early 1820s, by Giovanni Ferraro, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.This item is available to borrow from all library branches.
Resource Information
The item The Rise and Development of the Theory of Series up to the Early 1820s, by Giovanni Ferraro, (electronic resource) represents a specific, individual, material embodiment of a distinct intellectual or artistic creation found in University of Oklahoma Libraries.
This item is available to borrow from all library branches.
 Summary
 The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Most of the results derived from this time were derived using methods which would be found unacceptable today, and as a result, when one looks back to the theory of series prior to Cauchy without reconstructing internal motivations and the conceptual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a magician or diviner rather than the penetrating and complex work of great mathematicians. This monograph not only describes the entire complex of 17th and 18th century procedures and results concerning series, but it also reconstructs the implicit and explicit principles upon which they are based, draws attention to the underlying philosophy, highlights competing approaches, and investigates the mathematical context where the theory originated. The aim here is to improve the understanding of the framework of 17th and 18th century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some sense, to a unified theory that has come down to us today. Giovanni Ferraro is Professor of Mathematics and History of Mathematics at University of Molise
 Language

 eng
 eng
 Edition
 1st ed. 2008.
 Extent
 1 online resource (405 p.)
 Note
 Description based upon print version of record
 Contents

 From the beginnings of the 17th century to about 1720: Convergence and formal manipulation
 Series before the rise of the calculus
 Geometrical quantities and series in Leibniz
 The Bernoulli series and Leibniz’s analogy
 Newton’s method of series
 Jacob Bernoulli’s treatise on series
 The Taylor series
 Quantities and their representations
 The formalquantitative theory of series
 The first appearance of divergent series
 From the 1720s to the 1760s: The development of a more formal conception
 De Moivre’s recurrent series and Bernoulli’s method
 Acceleration of series and Stirling’s series
 Maclaurin’s contribution
 The young Euler between innovation and tradition
 Euler’s derivation of the Euler–Maclaurin summation formula
 On the sum of an asymptotic series
 Infinite products and continued fractions
 Series and number theory
 Analysis after the 1740s
 The formal concept of series
 The theory of series after 1760: Successes and problems of the triumphant formalism
 Lagrange inversion theorem
 Toward the calculus of operations
 Laplace’s calculus of generating functions
 The problem of analytical representation of nonelementary quantities
 Inexplicable functions
 Integration and functions
 Series and differential equations
 Trigonometric series
 Further developments of the formal theory of series
 Attempts to introduce new transcendental functions
 D’Alembert and Lagrange and the inequality technique
 The decline of the formal theory of series
 Fourier and Fourier series
 Gauss and the hypergeometric series
 Cauchy’s rejection of the 18thcentury theory of series
 Isbn
 9780387734682
 Label
 The Rise and Development of the Theory of Series up to the Early 1820s
 Title
 The Rise and Development of the Theory of Series up to the Early 1820s
 Statement of responsibility
 by Giovanni Ferraro
 Language

 eng
 eng
 Summary
 The theory of series in the 17th and 18th centuries poses several interesting problems to historians. Most of the results derived from this time were derived using methods which would be found unacceptable today, and as a result, when one looks back to the theory of series prior to Cauchy without reconstructing internal motivations and the conceptual background, it appears as a corpus of manipulative techniques lacking in rigor whose results seem to be the puzzling fruit of the mind of a magician or diviner rather than the penetrating and complex work of great mathematicians. This monograph not only describes the entire complex of 17th and 18th century procedures and results concerning series, but it also reconstructs the implicit and explicit principles upon which they are based, draws attention to the underlying philosophy, highlights competing approaches, and investigates the mathematical context where the theory originated. The aim here is to improve the understanding of the framework of 17th and 18th century mathematics and avoid trivializing the complexity of historical development by bringing it into line with modern concepts and views and by tacitly assuming that certain results belong, in some sense, to a unified theory that has come down to us today. Giovanni Ferraro is Professor of Mathematics and History of Mathematics at University of Molise
 http://library.link/vocab/creatorName
 Ferraro, Giovanni
 Dewey number
 515/.24309
 http://bibfra.me/vocab/relation/httpidlocgovvocabularyrelatorsaut
 COUr74VC4us
 Language note
 English
 LC call number
 QA2127
 Literary form
 non fiction
 Nature of contents
 dictionaries
 Series statement
 Sources and Studies in the History of Mathematics and Physical Sciences,
 http://library.link/vocab/subjectName

 Sequences (Mathematics)
 Mathematics
 Global analysis (Mathematics)
 History of Mathematical Sciences
 Sequences, Series, Summability
 Real Functions
 Analysis
 Label
 The Rise and Development of the Theory of Series up to the Early 1820s, by Giovanni Ferraro, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 363382) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 From the beginnings of the 17th century to about 1720: Convergence and formal manipulation  Series before the rise of the calculus  Geometrical quantities and series in Leibniz  The Bernoulli series and Leibniz’s analogy  Newton’s method of series  Jacob Bernoulli’s treatise on series  The Taylor series  Quantities and their representations  The formalquantitative theory of series  The first appearance of divergent series  From the 1720s to the 1760s: The development of a more formal conception  De Moivre’s recurrent series and Bernoulli’s method  Acceleration of series and Stirling’s series  Maclaurin’s contribution  The young Euler between innovation and tradition  Euler’s derivation of the Euler–Maclaurin summation formula  On the sum of an asymptotic series  Infinite products and continued fractions  Series and number theory  Analysis after the 1740s  The formal concept of series  The theory of series after 1760: Successes and problems of the triumphant formalism  Lagrange inversion theorem  Toward the calculus of operations  Laplace’s calculus of generating functions  The problem of analytical representation of nonelementary quantities  Inexplicable functions  Integration and functions  Series and differential equations  Trigonometric series  Further developments of the formal theory of series  Attempts to introduce new transcendental functions  D’Alembert and Lagrange and the inequality technique  The decline of the formal theory of series  Fourier and Fourier series  Gauss and the hypergeometric series  Cauchy’s rejection of the 18thcentury theory of series
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (405 p.)
 Form of item
 online
 Isbn
 9780387734682
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780387734682
 Specific material designation
 remote
 System control number

 (CKB)1000000000409094
 (EBL)337715
 (OCoLC)233971373
 (SSID)ssj0000773614
 (PQKBManifestationID)12299127
 (PQKBTitleCode)TC0000773614
 (PQKBWorkID)10846054
 (PQKB)10208902
 (SSID)ssj0000238439
 (PQKBManifestationID)11176025
 (PQKBTitleCode)TC0000238439
 (PQKBWorkID)10222588
 (PQKB)11770116
 (DEHe213)9780387734682
 (MiAaPQ)EBC337715
 (EXLCZ)991000000000409094
 Label
 The Rise and Development of the Theory of Series up to the Early 1820s, by Giovanni Ferraro, (electronic resource)
 Note
 Description based upon print version of record
 Bibliography note
 Includes bibliographical references (p. 363382) and index
 Carrier category
 online resource
 Carrier category code

 cr
 Content category
 text
 Content type code

 txt
 Contents
 From the beginnings of the 17th century to about 1720: Convergence and formal manipulation  Series before the rise of the calculus  Geometrical quantities and series in Leibniz  The Bernoulli series and Leibniz’s analogy  Newton’s method of series  Jacob Bernoulli’s treatise on series  The Taylor series  Quantities and their representations  The formalquantitative theory of series  The first appearance of divergent series  From the 1720s to the 1760s: The development of a more formal conception  De Moivre’s recurrent series and Bernoulli’s method  Acceleration of series and Stirling’s series  Maclaurin’s contribution  The young Euler between innovation and tradition  Euler’s derivation of the Euler–Maclaurin summation formula  On the sum of an asymptotic series  Infinite products and continued fractions  Series and number theory  Analysis after the 1740s  The formal concept of series  The theory of series after 1760: Successes and problems of the triumphant formalism  Lagrange inversion theorem  Toward the calculus of operations  Laplace’s calculus of generating functions  The problem of analytical representation of nonelementary quantities  Inexplicable functions  Integration and functions  Series and differential equations  Trigonometric series  Further developments of the formal theory of series  Attempts to introduce new transcendental functions  D’Alembert and Lagrange and the inequality technique  The decline of the formal theory of series  Fourier and Fourier series  Gauss and the hypergeometric series  Cauchy’s rejection of the 18thcentury theory of series
 Dimensions
 unknown
 Edition
 1st ed. 2008.
 Extent
 1 online resource (405 p.)
 Form of item
 online
 Isbn
 9780387734682
 Media category
 computer
 Media type code

 c
 Other control number
 10.1007/9780387734682
 Specific material designation
 remote
 System control number

 (CKB)1000000000409094
 (EBL)337715
 (OCoLC)233971373
 (SSID)ssj0000773614
 (PQKBManifestationID)12299127
 (PQKBTitleCode)TC0000773614
 (PQKBWorkID)10846054
 (PQKB)10208902
 (SSID)ssj0000238439
 (PQKBManifestationID)11176025
 (PQKBTitleCode)TC0000238439
 (PQKBWorkID)10222588
 (PQKB)11770116
 (DEHe213)9780387734682
 (MiAaPQ)EBC337715
 (EXLCZ)991000000000409094
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<div class="citation" vocab="http://schema.org/"><i class="fa faexternallinksquare fafw"></i> Data from <span resource="http://link.libraries.ou.edu/portal/TheRiseandDevelopmentoftheTheoryofSeries/S4LyMmh0g8/" typeof="Book http://bibfra.me/vocab/lite/Item"><span property="name http://bibfra.me/vocab/lite/label"><a href="http://link.libraries.ou.edu/portal/TheRiseandDevelopmentoftheTheoryofSeries/S4LyMmh0g8/">The Rise and Development of the Theory of Series up to the Early 1820s, by Giovanni Ferraro, (electronic resource)</a></span>  <span property="potentialAction" typeOf="OrganizeAction"><span property="agent" typeof="LibrarySystem http://library.link/vocab/LibrarySystem" resource="http://link.libraries.ou.edu/"><span property="name http://bibfra.me/vocab/lite/label"><a property="url" href="http://link.libraries.ou.edu/">University of Oklahoma Libraries</a></span></span></span></span></div>