The Calculus of Finite Differences

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American Mathematical Soc., Jan 1, 2000 - Difference equations. - 558 pages
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Contents

DIVIDED DIFFERENCES
1
DIFFERENCE OPERATORS
20
INTERPOLATION
55
NUMERICAL APPLICATIONS OF DIFFERENCES
87
RECIPROCAL DIFFERENCES
104
THE POLYNOMIALS OF BERNOULLI AND EULER
124
NUMERICAL DIFFERENTIATION AND INTEGRATION
154
CHAPTER VIII THE SUMMATION PROBLEM Consider the difference equation
200
FACTORIAL SERIES
271
CHAPTER XI THE DIFFERENCE EQUATION OF THE FIRST ORDER
322
GENERAL PROPERTIES OF THE LINEAR DIFFERENCE EQUATION
351
THE LINEAR DIFFERENCE EQUATION WITH CONSTANT COEFFICIENTS
384
THE LINEAR DIFFERENCE EQUATION WITH RATIONAL COEFFICIENTS OPERATIONAL METHODS
434
THE LINEAE DIFFERENCE EQUATION WITH RATIONAL COEFFICIENTS LAPLACES TRANSFORMATION
478
EQUATIONS WHOSE COEFFICIENTS ARE EXPRESSIBLE BY FACTORIAL SERIES
504
CHAPTER XVII THE THEOREMS OF POINCARE AND PERRON
523

THE PSI FUNCTION AND THE GAMMA FUNCTION
241

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