Does the confluent Heun function exist in Mathematica?

I try to evaluate the following,

DSolve[(1 - 2*M/r)^2*R''[r] + (1 - 2*M/r)*2*M/r^2*
R'[r] + (c^2 + 2*M*m^2/r)*R[r] == 0, R[r], r, Assumptions -> {m > 0, M > 0, c > 0}] 

but there are no results. Also, using Maple, my friend show that the solutions is confluent Heun function. Can anybody help me to understand what I do wrong?


1 Answer 1


The 5 Heun functions will be available in version 12.1 of Mathematica, so that we will be able to solve Heun-type of equations in build-in Mathematica functions.

  • 2
    $\begingroup$ This is certainly something to look forward to; as noted in the comments, there have been situations where Maple's support for Heun functions has made it more helpful than Mathematica. $\endgroup$ Feb 3, 2020 at 11:40

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