Elliptic-function sentence example

elliptic-function
  • ch (2n +1)I 7 ry /a yl-R3ct (2n +I)3.ch(2n+I)17b /a ' 16 cos(2n+I) 2 7 z /a w1=4,i+ 4, ii = iR ?3a2 an elliptic-function Fourier series; with a similar expression for 1,'2 with x and y, a and b interchanged; and thence 4, = '1 +h.
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  • 2, so that is an elliptic function of t, except when c =a, or 3a.
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  • Clebsch to take the form T= 2p(x12 +x22)+2p'x32 + q (xiyi +x2y2) +q'x3y3 +2r(y12+y22)+2r'y32 so that a fourth integral is given by dy 3 /dt = o, y = constant; dx3 (4 y) (q + y) _ (y y) dt - xl 'x2 xl Y Y x l 2 - 1, y2 () = (x12 +x22) (y12 + y22) = (X 1 2 + X 2) +y22)-(FG-x3y3)2 = (x 1 y32-G2)-(Gx3-Fy3) 2, in which 2 = F 2 -x3 2, x l y l +x2y2 = FG-x3y3, Y(y1 2 +y2 2) = T -p(x12 +x22) -p'x32 -2q(xiyi 'x2y2)- 2 q ' x = (p -p') x 2 + 2 (- q ') x 3 y 3+ m 1, (6) m1 = T 2 i y 3 2 (7) so that dt3) 2 =X3, (8) where X3 is a quartic function of x3, and thus t is given by an elliptic (8) (6) (I) integral of the first kind; and by inversion x 3 is in elliptic function of the time t.
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  • sin o= F dl, (20) C3 do F2 h _ F2 cos 2 o F 2 sin z o F dt y - V C G c +2 c1 coso+H]; (21) 1 z so that cos 0 and y is an elliptic function of the time.
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  • In the solution the value of an elliptic function is found by means of the arithmetico-geometrical mean.
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