## 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

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書名 Tables for the use of elliptic functions by Tadahiko Kubota 窪田 忠彦 Tohoku Imperial University 1919 75 p. 25 cm 英語
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