By considering special exponential series arising in number theory, the authors derive the generalized Euler-Jacobi series, expressed in terms of hypergeometric series. They then employ Dingle's theory of terminants to show how the divergences in both dominant and subdominant series of a complete asymptotic expansion can be tamed. The authors use numerical results to show that a complete asymptotic expansion can be made to agree with exact results for the generalized Euler-Jacobi series to any desired degree of accuracy.
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'The book is of considerable value for the number theorist and for the analyst as well.' Monatshefte für Mathematik
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In many real physical problems an exact solution cannot be obtained, and only approximations called asymptotic expansions exist. This work presents exciting new developments, previously neglected, in understanding the subdominant exponential terms of these expansions.
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First Sentence:
The imaginary transformation, q(t) to q(it), enables the Jacobi theta function 03(z\q(t)) to be recast as where z is any arbitrary complex variable and the complex variable t obeys the condition Ret > 0. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Meijer G-function, Academic Press, Cambridge University Press New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
The imaginary transformation, q(t) to q(it), enables the Jacobi theta function 03(z\q(t)) to be recast as where z is any arbitrary complex variable and the complex variable t obeys the condition Ret > 0. Read the first page Key Phrases - Capitalized Phrases (CAPs): (learn more)
New York, Meijer G-function, Academic Press, Cambridge University Press New!
Concordance | Text Stats Browse Sample Pages:
Front Cover | Table of Contents | First Pages | Index | Back Cover | Surprise Me!
Citations (learn more)
This book cites 11
books:
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cites this book:
- A Treatise on the Theory of Bessel Functions (Cambridge Mathematical Library) by G. N. Watson on page 116
- Divergent Series (AMS Chelsea Publishing) by G. H. Hardy on page 115
- Brief Introduction to Theta Functions by Bellman on page 115
- Theory and Application of Infinite Series (Dover Books on Mathematics) by Konrad Knopp on page 115
- Asymptotic and Computational Analysis (Lecture Notes in Pure and Applied Mathematics) by R. Wong on page 116
See all 11 books this book cites
- Ramanujan's Notebooks, Part V by Bruce C. Berndt in Back Matter
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