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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?

J. M.'s missing motivation
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Artem Alexandrov
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  • Related: https://mathematica.stackexchange.com/questions/94856/differential-equation-solution, https://mathematica.stackexchange.com/questions/139428/what-are-the-limitation-on-current-mathematicas-ability-to-solving-a-sturm-liou – Michael E2 Jan 28 '20 at 17:16
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    Currently, the Heun functions aren't yet implemented in Mathematica. – J. M.'s missing motivation Jan 28 '20 at 17:16
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    Maple is more advanced in the solution of Differential Equations than Mathematica. – Mariusz Iwaniuk Jan 28 '20 at 17:18
  • What does this differential equation describe? What are initial/boundary conditions? – Artes Jul 12 '20 at 02:10
  • @Artes mentioned equation describes a dynamical proccess with black hole background – Artem Alexandrov Jul 12 '20 at 11:30
  • @ArtemAlexandrov I've expected that, I have provided here a few answers related to Schwarzschild geometry e.g. 1, 2. Would you mind adding more details and specifying a bit what kind of process is it? Why is this equation linear, does it follow a linearization procedure or just by chance? – Artes Jul 12 '20 at 14:06
  • @ArtemAlexandrov Could you add more details and specify what kind of process is it or send appropriate link? How could this equation be derived? – Artes Jul 13 '20 at 23:23
  • Unfortunately, even tho the Heun functions are now built-in, DSolve[] still returns a DifferentialRoot[] solution... – J. M.'s missing motivation Dec 24 '20 at 15:37

1 Answers1

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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.

Tigran Ishkhanyan
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    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. – J. M.'s missing motivation Feb 03 '20 at 11:40