Screen LibraryGamma : exploring Euler's constant /
"Among the many constants that appear in mathematics, [pi], e, and i are the most familiar. Following closely behind is [gamma] or gamma, a constant that arises in many mathematical areas yet remains profoundly mysterious. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who fi...
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| Main Authors: | |
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| Published: |
Princeton University Press,
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| Publisher Address: | Princeton, N.J. : |
| Publication Dates: | [2003] |
| Literature type: | Book |
| Language: | English |
| Series: |
Princeton science library
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| Subjects: | |
| Summary: |
"Among the many constants that appear in mathematics, [pi], e, and i are the most familiar. Following closely behind is [gamma] or gamma, a constant that arises in many mathematical areas yet remains profoundly mysterious. Introduced by the Swiss mathematician Leonhard Euler (1707-1783), who figures prominently in this book, gamma is defined as the limit of the sum of 1 + 1/2 + 1/3 + ... up to 1/n , minus the natural logarithm of n -- and the numerical value is 0.5772156 ... But unlike its more celebrated colleagues [pi] and e, the exact nature of gamma remains a mystery. In fact, we don't even know if gamma is a fraction. In this tantalizing blend of history and mathematics, Julian Havil takes readers on a journey through logarithms and the harmonic series, the two defining elements of gamma, toward the first account of gamma's place in mathematics. Sure to be popular with not only students and instructors but all math aficionados, Gamma takes us through countries, centuries, lives, and works, unfolding along the way the stories of some remarkable mathematics from some remarkable mathematicians."--Back cover. |
| Item Description: | "New Princeton science library paperback printing, 2018" |
| Carrier Form: | xxiii, 266 pages : illustrations, forms ; 22 cm. |
| Bibliography: | Includes bibliographical references (pages 255-258) and indexes. |
| ISBN: |
9780691178103 (paperback) : 0691178100 (paperback) |
| Index Number: | QA29 |
| CLC: | O115.22 |
| Call Number: | O115.22/H388 |
| Contents: | The logarithmic cradle -- The harmonic series -- Sub-harmonic series -- Zeta functions -- Gamma's birthplace -- The Gamma function -- Euler's wonderful identity -- A promise fulfilled -- What is gamma... exactly ? -- Gamma as a decimal -- Gamma as a fraction -- Where is Gamma ? -- It's a harmonic world -- It's a logarithmic world -- Problems with primes -- The Riemann initiative -- Appendix A the Greek alphabet -- Appendix B big oh notation -- Appendix C Taylor expansions -- Appendix D complex function theory -- Appendix E application to the Zeta function -- References -- Name index -- Subject index. |