Gamma Function,Beta Function,generalization of the binomial coefficient, integral,transformation,Relation Between Gamma Function and Sine Function, Duplication Formula for the Gamma Function.

The product formula, Euler's integrals, Euler's constant, The Gamma function has the product formulas , Consequences of the product formula, Stirling approximation , The logarithmic derivative.

Lattices, doubly periodic functions, vector space, partial summation, p-adic integers, A doubly-periodic holomorphic function is constant, holomorphic differentials,The sum of the residues of any meromorphic differential, meromorphi...

Elliptic Functions,Rectification of Ellipse, the equation of
a general ellipse, elliptic integrals, equation of the conservation of energy ,differential equation, Jacobi, the elliptic sine function of Jacobi, Interchangeability of Cub...