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Hypergeometric Solutions of Second Order Linear Differential Equations

Tech ID:
Principal Investigator:
Dr. Mark van Hoeij
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Researchers, scientists, and engineers across a wide range of fields of expertise depend on computer algebra systems to solve complex equations such as linear differential or difference equations. Solutions to these equations cannot often be expressed by a closed-form expression. Functions are in closed form if they are written in terms of commonly used functions such as exp and log. Using computer systems to solve equations that cannot be expressed by a closed-form expression leads to an error or no solution being found. This can lead one to believe that there is no solution to the equation, even if this is not the case.

Dr. Mark van Hoeij has extensively research unsolvable equations such as second order linear differential equations. He has created a novel algorithm to find closed form solutions to previously unsolvable equations. This state of the art algorithm can be implemented into current computer algebra systems.


  • State of the art algorithm to find solutions not readily available
  • Easily integrated with current software