In this paper we deal with the following problems: When do the solutions of a collection of differential equations satisfy an elementary relation, that is, when is there an equation of the form R = 0 ...

The statistical physics of graphs and partition functions represents a vibrant intersection of graph theory, statistical mechanics and computational complexity. By summing over an ensemble of ...

A function is a rule that is applied to one set of values to give another set of values. A function can be illustrated on a graph – points are plotted as coordinates and joined by either a straight ...

All quadratic functions have the same type of curved graphs with a line of symmetry. The graph of the quadratic function \(y = ax^2 + bx + c \) has a minimum turning point when \(a \textgreater 0 \) ...

It is well known that the hypergeometric functions $_2F_1 (\alpha \pm 1, \beta, \gamma; t), _2F_1(\alpha, \beta \pm 1, \gamma; t), \quad _2F_1 (\alpha, \beta, \gamma \pm 1; t),$ which are continguous ...