Heun functions arise in the solutions of various differential equations, for instance for the Schroedinger equation for the hydrogen atom in physics, which is also of chemical interest. Although they have been nominally included in Maple for several years, they are still in a primitive state; despite their obscurity and intractable nature, there seems not to exist much possibility, within Maple, to convert these functions into better known and characterised functions. A similar condition holds for Lame and spheroidal functions that are invaluable in the solution of differential equations in physics but are not even mentioned in Maple.
The compilation of mathematical functions by Abramowitz and Stegun was published half a century ago, but there are still important functions explained therein that are lacking from Maple, not to mention the successor in the NIST Digital Library of Mathematical Functions.
Integral equations are another weak component of Maple; the present content relies on a basis of work of ProfessorCorless and his student submitted to the 'Maple Share Library' -- decades ago. Forty years ago, David Stoutemyer generated some procedures to solve non-linear integral equations in Reduce, but forty years later Maple has no benefit from that knowledge.
We can only hope that Maple 19 will remedy some of these gross deficiencies. The teaching, learning and practice of physics will benefit from their implementation.