View source for Book:Harris Hancock/Lectures on the theory of elliptic functions

{{Book|Lectures on the theory of elliptic functions|1910|||Harris Hancock}}

===Online copies===
[https://archive.org/details/lecturestheorell00hancrich hosted by archive.org]<br />

===Contents===
:CHAPTER 1 PRELIMINARY NOTIONS
:::1. One-valued function. Regular function. Zeros
:::2. Singular points. Pole or infinity
:::3. Essential singular points
:::4. Remark concerning the zeros and poles
:::5. The point at infinity
:::6. Convergence of series
:::7. A one-valued function that is regular at all points of the plane is a constant
:::8. The zeros and the poles of a one-valued function are necessarily isolated
::Rational functions
:::9.
:::10.
::Principal Analytical Forms of Rational Functions
:::11. <i>First form:</i> Where the poles and the corresponding principal parts are brought into evidence
:::12. <i>Second form:</i> Where the zeros and the infinities are brought into evidence
::Trigonometric functions
:::13. Integral transcendental functions
:::14. Results established by Cauchy
:::15.
:::16.
::Infinite products
:::17. 
:::18. 
:::19. The infinite products expressed through infinite series
:::20. 
:::21. 
:::22. The cot-function
:::23. Development in series
::The General Trigonometric Functions
:::24. The general trigonometric function expressed as a rational function of the cot-function
:::25. Decomposition into partial fractions
:::26. Expressed as a quotient of linear factors
:::27. Domain of convergence. Analytic continuation
:::28. Example of a function which has no definite derivative
:::29. The function is one-valued in the plane where the canals have been drawn
:::30. The process may be reversed
:::31. Algebraic addition-theorems. Definition of an elliptic function
:::Examples
:CHAPTER II FUNCTIONS WHICH HAVE ALGEBRAIC ADDITION-THEOREMS
:::32. Examples of functions having algebraic addition-theorems
:::33. The addition-theorem stated
:::34. Méray's eliminant equation
:::35. The existence of this equation is universal for functions considered
:::36. A formula of fundamental importance for the addition-theorems
:::37. The higher derivatives expressed as rational functions of the function and its first derivative
:::37a. 
:::38. 
:::39. A form of the general integral of Méray's equation
::The Discussion Restricted to One-valued Functions
:::40. All functions which have the property that $\phi(u+v)$ may be rationally expressed through $\phi(u)$, $\phi'(u)$, $\phi(v)$, $\phi'(v)$ are one-valued
:::41. 
:::42. 
:::43. 
:::44. 
:::45. 
:::46. Example showing that a function $\phi(u)$ may be such that $\phi(u+v)$ is rationally expressible through $\phi(u)$, $\phi'(u)$, $\phi(v)$, $\phi'(v)$ without having an algebraic addition-theorem
::Continuation of the Domain in which the Analytic Function $\phi(u)$ has been Defined, with Proofs that its Characteristic Properties are Retained in the Extended Domain
:::47. Definition of the function in the neighborhood of the origin
:::48. 
:::49. 
:::50. 
:::51. The other characteristic properties of the function are also retained. The addition-theorem, while limited to a ring-formed region, exists for the whole region of convergence established for $\phi(u)$

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