复函数论中的经典论题-(影印版)

本书特色

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　　in addition to the correction of typographical errors， the text has been materially changed in three places. the derivation of stirling’s formula in chapter 2.4， now follows the method of stieltjes in a more systematic way. the proof of picard’s little theorem in chapter 10， 2， is carried out following an idea of h. konig. finally， in chapter 11， 4， an inaccuracy has been corrected in the proof of szego’s theorem.

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目录

preface to the second german editionpreface to the first german editionacknowledgmentsadvice to the readera infinite products and partial fraction series1 infinite products of holomorphic functions1. infinite products1. infinite products of numbers2. infinite products of functions2. normal convergence1. normal convergence2. normally convergent products of holomorphic functions3. logarithmic difi.erentiation3. the sine product sin πz =πz ∏∞v=1(1-z2/v2)1. standard proof2. characterization of the sine by the duplication formula3. proof of euler’s formula using lemma 24. proof of the duplication formula for euler’s product, followingeisenstein5. on the history of the sine product4. euler partition products1. partitions of natural numbers and euler products2. pentagonal number theorem. recursion formulas for p(n) andσ(n)3. series expansion of ∏∞v=1(1+ qvz) in powers of z4. on the history of partitions and the pentagonal numbertheorem5*. jacobi’s product representation of theseriesj(z,q):=∑∞v=-∞qv2zv1. jacobi’s theorem2. discussion of jacobi’s theorem3. on the history of jacobi’s identitybibliographythe gamma function1. the weierstrass function △(z) = zeγz ∏v≥1(1+z/v)e-z/v1. the auxiliary functionh(z):= z∏∞v(1+z/v)e-z/v2. the entire function △(z):=eγzh(z)2. the gamma function1. properties of the f-function2. historical notes3. the logarithmic derivative4. the uniqueness problem5. multiplication formulas6. h(o)lder’s theorem7. the logarithm of the f-function3. euler’s and hankel’s integral representations of γ(z)1. convergence of euler’s integral2. euler’s theorem3. the equation4. hankel’s loop integral4. stirling’s formula and gudermann’s series1. stieltjes’s definition of the function μ(z)2. stirling’s formula3. growth of |γ(x+iy)|for |y|→∞4. gudermann’s series5. stirling’s series6. delicate estimates for the remainder term7. binet’s integral8. lindel(o)f’s estimate5. the beta function1. proof of euler’s identity2. classical proofs of euler’s identitybibliography……b mapping theoryc selectashort biographiessymbol indexname indexsubject index

封面

书名:复函数论中的经典论题-(影印版)

作者:雷默特

页数:349

定价:¥59.0

出版社:世界图书出版公司

出版日期:2013-03-01

ISBN:9787510058288

PDF电子书大小:64MB 高清扫描完整版