Siegel G-function
Encyclopedia
In mathematics, a Siegel G-function is a class of functions in transcendence theory
introduced by C. L. Siegel. They satisfy a linear differential equation
with polynomial
coefficients, and the coefficients of their power series expansion lie in a fixed algebraic number field
and have heights of at most exponential growth.
Transcendence theory
Transcendence theory is a branch of number theory that investigates transcendental numbers, in both qualitative and quantitative ways.-Transcendence:...
introduced by C. L. Siegel. They satisfy a linear differential equation
Linear differential equation
Linear differential equations are of the formwhere the differential operator L is a linear operator, y is the unknown function , and the right hand side ƒ is a given function of the same nature as y...
with polynomial
Polynomial
In mathematics, a polynomial is an expression of finite length constructed from variables and constants, using only the operations of addition, subtraction, multiplication, and non-negative integer exponents...
coefficients, and the coefficients of their power series expansion lie in a fixed algebraic number field
Algebraic number field
In mathematics, an algebraic number field F is a finite field extension of the field of rational numbers Q...
and have heights of at most exponential growth.