Let y(z)=2sinh−1(z/(2a)1/2)(z2+2a)1/2
where sinh(z) is the sine hyperbolic function.
K(z):=1z(y(z)−y(−z))→1/2az2+1/6−z290a+z4378a2−23z628350a3+263z8935550a4−133787z101277025750a5+157009z123831077250a6−16215071z14976924698750a7+2689453969z16389792954801250a8+O(z18)
How can I find the linear differential equation in ∂∂z with coefficent in the polynomial ring C[z] that annihilates K(z). I am unable to do it by hand I think some software in sagemath might help.