THE GAUSS HYPERGEOMETRIC FUNCTION: RELATIONS TO OTHER FUNCTIONS
Abstract
This study briefly discusses differential equations, types of differential equations: ordinary differential equations and partial differential equations; order and degree of
differential equations; methods of solution of first order equations, such as separation
of variables, exact, and integrating factors. For second order differential equations,
we discuss homogeneous equations and nonhomogeneous equations. We discuss and
mention the characteristics equations and linear combination (linear independence) in
the case of second order differential equations with constant coefficients. In the nonhomogeneous case, we discuss methods of solution, such as, method of undetermined
coefficients, method of variation of parameters, and the power series method. The
main focus of the study is the Gauss hypergeometric equation, which is a second order
ordinary differential equation with variable coefficients. Using the Frobenius method,
we obtain a solution known as the Gauss hypergeometric function. Relations of the
Gauss hypergeometric relation to other elementary functons, such as, logarithmic,
exponential, and trigonometric functions are also considered.
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