Notes On The Binomial Transform: Theory And Table With Appendix On Stirling Transform
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A01=Khristo N Boyadzhiev
Author_Khristo N Boyadzhiev
Bernoulli Numbers
Binomial Coefficients
Binomial Identities
Binomial Sums
Binomial Transform
Category=PBH
Discrete Mathematics
eq_isMigrated=1
eq_isMigrated=2
eq_nobargain
Euler's Series Transformation
Exponential Polynomials
Fibonacci Numbers
Finite Differences
Geometric Polynomials
Harmonic Numbers
Laguerre Polynomials
Melzak's Formula
Special Numbers and Polynomials
Stirling Numbers of the First Kind
Stirling Numbers of the Second Kind
Stirling Transform
Trigonometric Integrals
Product details
- ISBN 9789813234970
- Publication Date: 30 May 2018
- Publisher: World Scientific Publishing Co Pte Ltd
- Publication City/Country: SG
- Product Form: Hardback
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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.
