Tables for the use of elliptic functions

[目次]

  • Contents
  • I. Weierstrassian elliptic functions.
  • 1. Fundamental theorems. / 1
  • 2. The function ϑu. / 2
  • 3. ζ and σ functions. / 3
  • 4. Addition theorems of ζu and ϑu. / 6
  • 5. Representation of elliptic functions in terms of sigma functions. / 8
  • 6. Representation of elliptic functions by ζ functions. / 9
  • 7. Functions σ1u,σ2u,σ3u. / 10
  • 8. Relations between σu,σ1u,σ2u,σ3u. / 12
  • 9. Formulae for σ quotients. / 14
  • 10. Some relations between σ functions. / 15
  • 11. Relations between Weierstrassian and Jacobian elliptic functions. / 15
  • 12. Infinite products for σ functions. / 18
  • 13. Further relations to Jacobi's elliptic functions. / 19
  • 14. Addition theorems for σ Functions. / 20
  • 15. Representation of certain radical quantities by infinite products. / 24
  • 16. Degeneration of elliptic functions. / 25
  • 17. Reality of ϑu. / 26
  • II. Jacobian elliptic functions.
  • 1. Reduction of elliptic integrals. / 27
  • 2. Addition theorems of sn u,cn u,dn u. / 31
  • 3. Multiplication and division. / 34
  • 4. Functions Εu,Ζu,Θu and Π(u,a). / 36
  • 5. Function Hu. / 38
  • 6. Transformation of elliptic integrals. / 41
  • 7. Theta functions. / 43
  • 8. Infinite products for theta functions. / 45
  • 9. Jacobi's imaginary transformations. / 46
  • 10. Introduction of sn u,cn u,dn u. / 46
  • 11. Theta relations. / 47
  • 12. Second method of defining sn,cn,dn. / 51
  • 13. Jacobi's ζ functions. / 54
  • 14. Jacobi's notation in "Fundamenta Nova." / 58
  • 15. Relations to Weierstrassian elliptic functions. / 59
  • 16. Table for the special values of argument in Θu,Ζu,Ηu. / 60
  • 17. Expansions into power series and Fourier's Series. / 61
  • 18. Table for comparison of various notations. / 62
  • 19. Numerical tables. / 63

「国立国会図書館デジタルコレクション」より

この本の情報

書名 Tables for the use of elliptic functions
著作者等 by Tadahiko Kubota
窪田 忠彦
Tohoku Imperial University
出版元 Tohoku Imperial University
刊行年月 1919
ページ数 75 p.
大きさ 25 cm
言語 英語
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