Elliptic Functions: An Elementary Text-book for Students of Mathematics |
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Elliptic Functions - An Elementary Text-Book for Students of Mathematics Arthur L. Baker No preview available - 2009 |
Elliptic Functions: An Elementary Text-Book for Students of Mathematics Arthur Latham Baker No preview available - 2018 |
Elliptic Functions. An Elementary Text-book for Students of Mathematics Arthur Latham Baker No preview available - 2018 |
Common terms and phrases
4K+u a. c. log amplitude angle Applying eq Chap CHAPTER cn 2u cn iu cn u dn cn² complete function cos² Crelle's Journal decreasing series dn 2u dn iu dx x² e-zix Elliptic Functions Elliptic Integrals equation equation 21 equations 14 EXAMPLE F(kn F(kon factors find q gives Hence hyperbola Jacobi k sin k'on k₁ k₂ k² sin² k² sn k²x² ksin LANDEN'S TRANSFORMATION Legendre limiting value log log log q log tan 45 Method modulus q²h rational function repeated applications series of moduli sin sin sin sin² sin³ Ø sn 2K sn² Substituting in eq Substituting these values tan² tn iu trigonometric functions values in eq whence x'dx x²+a x2m dx Δμ ΔΦ π π πικ πω Φι аф
Popular passages
Page 1 - English mathematician, published his celebrated theorem showing that any arc of a hyperbola may be measured by two arcs of an ellipse, an important element of the theory of Elliptic Functions, but then an isolated result.
Page 41 - Taking for 0, — ф, etc., not always the least angle given by the tables, but that which is nearest to ф. BISECTED AMPLITUDES. We have identically - = 2.-r = 2F\k,am - ; etc. Therefore и = F(k, am u) = 2"F\k, am -j = 2" . am- , (« = limit,) 7/ am - being determined by repeated applications of eq.
Page 5 - J. dx which are called elliptic integrals of the first, second, and third order.