hello, The argument x is the geometric surface of the squircle generated by the equation x ^ 4 + y ^ 4 = 1. I thought about it for a long time, and in my humble opinion it seems to be a kind of angle from one axis. the values resulting from the integrals of the inverse functions lead me to believe it I searched for a link with ordinary trigonometric functions in vain and I do not know if there are any. Best regards Le jeudi 26 avril 2018 à 21:48:15 UTC+1, Allan Wechsler <acwacw@gmail.com> a écrit : 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