Miller K.S. An Introduction to the Calculus of Finite Differences and Difference Equations

New York: Dover Publications, 1960. — 174 p.The Calculus of Finite DifferencesThe difference calculus
Factorial polynomials
Stirling numbers
Newton's formula
The indefinite sum
The definite sum
ExercisesInfinite ProductsInfinite products
The associated logarithmic series
Absolute convergence
Infinite products of functions
The infinite product representation of the sine function
The Gamma function
The Beta function
The infinite product representation of the Gamma function
Finite differences and the Gamma function
ExercisesBernoulli Numbers and PolynomialsGenerating function for the Bernoulli polynomials
The Bernoulli numbers
Properties of the Bernoulli polynomials
Further properties of the Bernoulli functions
Power series expansion for tangent and cotangent
The Euler-Maclaurin formula Preliminary remarks
Derivation of the Euler-Maclaurin formula
Asymptotic expansions
An application of the Euler-Maclaurin formula
Stirling's formula
The algebra of operators
ExercisesLinear Difference Equations in the Real DomainSpecial formulas
Linear difference equations
The nonhomogeneous equation
Further comments on linear equations
Linear equations with constant coefficients
Exercises