I understand that this is intended as a variation of the ordinary trigonometric functions, but with the "squircle" x^4 + y^4 = 1 taking the role of the circle. What I don't understand is what the argument x represents. Is it still the angle from one axis? Or is it some strange function of the angle? On Thu, Apr 26, 2018 at 4:35 PM, françois mendzina essomba2 via math-fun < math-fun@mailman.xmission.com> wrote:
I noticed an error in my last post correction of derivations
diff(qanh(x),x)=1/(qosh(x))^2;diff(cqnh(x),x)=-1/(qinh(x))^2;
limited development of functions to order 16; I found
qosh(x)=1+(1/4)*x^4+(9/160)*x^8+(149/9600)*x^(12)+(15147/3328000)*x^16; qinh(x)=x+(3/20)*x^5+(19/480)*x^9+(469/41600)*x^13+(189611/56576000)*x^17;
I deduce without verifying that:
qos(x)=1-(1/4)*x^4+(9/160)*x^8-(149/9600)*x^(12)+(15147/3328000)*x^16; qin(x)=x-(3/20)*x^5+(19/480)*x^9-(469/41600)*x^13+(189611/56576000)*x^17; _______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun