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
刊行年月 1919
ページ数 75 p.
大きさ 25 cm
言語 英語
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