Maple V R5’s expression for the partial derivative of JacobiDN with respect to its second argument is incorrect (the sign of the ﬁrst summand is wrong, see below). A workaround is to substitute all occurrences of JacobiDN(u,k) in an expression which is to be diﬀerentiated with sqrt(1-k^2*JacobiSN(u,k)^2), and then diﬀerentiate.
In the following,
dj(u,k) returns Maple’s incorrect expression for the derivative,
cdj(u,k) returns Maple’s expression but with a minus sign before the ﬁrst summand inserted by hand,
ndj(u,k,h) approximates the derivative by the standard diﬀerence quotient with step h, and
sdj(u,k) returns an expression computed using the workaround suggested above:
See also: Bug in Jacobi elliptic function
It is corrected with Maple 7 (U. Klein)