About the Book
Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Pages: 59. Chapters: Modular forms, Elliptic function, Frobenius solution to the hypergeometric equation, Mock modular form, Weierstrass's elliptic functions, Modular group, Theta function, Moduli space, Geometric invariant theory, ELSV formula, Hilbert scheme, J-invariant, Eisenstein series, Teichmuller space, Modular curve, Modularity theorem, Stable map, Tau-function, Classical modular curve, Fundamental pair of periods, Hecke operator, Congruence subgroup, Moduli of algebraic curves, Hard hexagon model, Schwarzian derivative, Ribet's theorem, Dedekind eta function, Real analytic Eisenstein series, Dedekind sum, Serre conjecture, Character variety, Siegel modular form, Rogers-Ramanujan continued fraction, Picard-Fuchs equation, Cusp form, Rogers-Ramanujan identities, Ramanujan-Petersson conjecture, Weil-Petersson metric, Upper half-plane, Poincare series, Modular lambda function, Automorphic factor, Hodge bundle, Quantum ergodicity, Kronecker limit formula, Torelli theorem, Petersson inner product, Atkin-Lehner theory, Modular equation, Moduli scheme, Jacobi form, Artin approximation theorem, Maass wave form, Eisenstein ideal, Eichler-Shimura congruence relation, Lemniscatic elliptic function, Equianharmonic, Elliptic unit, Overconvergent modular form, Formal moduli, Shimura correspondence, J-line. Excerpt: In the following we solve the second-order differential equation called the hypergeometric differential equation using Frobenius method, named after Ferdinand Georg Frobenius. This is a method that uses the series solution for a differential equation, where we assume the solution takes the form of a series. This is usually the method we use for complicated ordinary differential equations. The solution of the hypergeometric differential equation is very important. For instance, Legendre's differential equation can be shown to be a ...
