The binomial transform is a discrete transformation of one sequence
into another with many interesting applications in combinatorics
and analysis. This volume is helpful to researchers interested in
enumerative combinatorics, special numbers, and classical analysis.
A valuable reference, it can also be used as lecture notes for a
course in binomial identities, binomial transforms and Euler series
transformations. The binomial transform leads to various
combinatorial and analytical identities involving binomial
coefficients. In particular, we present here new binomial
identities for Bernoulli, Fibonacci, and harmonic numbers. Many
interesting identities can be written as binomial transforms and
vice versa.The volume consists of two parts. In the first part, we
present the theory of the binomial transform for sequences with a
sufficient prerequisite of classical numbers and polynomials. The
first part provides theorems and tools which help to compute
binomial transforms of different sequences and also to generate new
binomial identities from the old. These theoretical tools (formulas
and theorems) can also be used for summation of series and various
numerical computations.In the second part, we have compiled a list
of binomial transform formulas for easy reference. In the Appendix,
we present the definition of the Stirling sequence transform and a
short table of transformation formulas.
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