Terms of the power series for the hyperbolic square in the form z = f(x, y). Note that the fractions are not reduced; their denominators are the odd part of the factorial of the total degree. Notice also that the first and last coefficients of each degree are those of the series for the tangent.

xy +

1/3xy³ + 1/3x³y +

2/15xy⁵ + 10/15x³y³ + 2/15x⁵y +

17/315xy⁷ + 245/315x³y⁵ + 245/315x⁵y³ + 17/315x⁷y +

62/2835xy⁹ + 1974/2835x³y⁷ + 5418/2835x⁵y⁵ +1974/2835x⁷y³ + 62/2835x⁹y +

1382/155925xy¹¹ + 82830/155925x³y⁹ + 480942/155925x⁵y⁷ + 480942/155925x⁷y⁵ + 82830/155925x⁹y³ + 1382/155925x¹¹y +

21844/6081075xy¹³ + 2214212/6081075x³y¹¹ + 23407956/6081075x⁵y⁹ + 48990084/6081075x⁷y⁷ + 23407956/6081075x⁹y⁵ + 2214212/6081075x¹¹y³ + 21844/6081075x¹³y +

929569/638512875xy¹⁵ + 147610645/638512875x³y¹³ + 2573471901/638512875x⁵y¹¹ + 9684402585/638512875x⁷y⁹ + 9684402585/638512875x⁹y⁷ + 2573471901/638512875x¹¹y⁵ + 147610645/638512875x¹³y³ + 929569/638512875x¹⁵y +

6404582/10854718875xy¹⁷ + 1504380830/10854718875x³y¹⁵ + 40303529994/10854718875x⁵y¹³ + 247206099998/10854718875x⁷y¹¹ + 442771035850/10854718875x⁹y⁹ + 247206099998/10854718875x¹¹y⁷ + 40303529994/10854718875x¹³y⁵ + 1504380830/10854718875x¹⁵y³ + 6404582/10854718875x¹⁷y +

443861162/1856156927625xy¹⁹ + 147504515298/1856156927625x³y¹⁷ + 5758566225138/1856156927625x⁵y¹⁵ + 53719279799250/1856156927625x⁷y¹³ + 156014422236530/1856156927625x⁹y¹¹ + 156014422236530/1856156927625x¹¹y⁹ + 53719279799250/1856156927625x¹³y⁷ + 5758566225138/1856156927625x¹⁵y⁵ + 147504515298/1856156927625x¹⁷y³ + 443861162/1856156927625x¹⁹y