Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 967-976. https://doi.org/10.12988/imf.2014.4492

A method is presented, with standard examples, based on an elementary complex integral expression, for developing, in particular, series solutions for second-order linear homogeneous ordinary differential equations. Straightforward to apply, the meth... Read More about Series Solution of Second-Order Linear Homogeneous Ordinary Differential Equations via Complex Integration.

On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. (2014)
Journal Article
Robin, W. (2014). On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method. Nonlinear Analysis and Differential Equations, 2, 155-171. https://doi.org/10.12988/nade.2014.4712

The theory of series solutions for two important classes of the general higher-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression derived and applied in previous papers [10,... Read More about On the procedure for the series solution of certain general-order homogeneous linear differential equations via the complex integration method..

On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method (2014)
Journal Article
Robin, W. (2014). On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method. Nonlinear Analysis and Differential Equations, 2(4), 173-188. https://doi.org/10.12988/nade.2014.4713

The theory of series solutions for second-order linear homogeneous ordinary differential equation is developed ab initio, using an elementary complex integral expression (based on Herrera’ work [3]) derived and applied in previous papers [8, 9]. As w... Read More about On the procedure for the series solution of second-order homogeneous linear differential equation via the complex integration method.

Ladder-Operator Factorization and the Bessel Differential Equations (2014)
Journal Article
Robin, W. (2014). Ladder-Operator Factorization and the Bessel Differential Equations. International Mathematical Forum, 9, 71-80. https://doi.org/10.12988/imf.2014.311214

We present an alternative approach to the discussion of Bessel equations and Bessel functions, through an elementary factorization method. The various Bessel equations are represented by a single parameterized form and, after a standard transformatio... Read More about Ladder-Operator Factorization and the Bessel Differential Equations.

Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration (2014)
Journal Article
Robin, W. (2014). Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration. International Mathematical Forum, 9, 953-965. https://doi.org/10.12988/imf.2014.4491

A method is presented (with standard examples) based on an elementary complex integral expression, for developing Frobenius series solutions for second-order linear homogeneous ordinary Fuchs differential equations. The method reduces the task of fin... Read More about Frobenius Series Solution of Fuchs Second-Order Ordinary Differential Equations via Complex Integration.