The Partition Method for a Power Series Expansion Theory and Applications 1st Edition by Victor Kowalenko 0128045114 9780128045114

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Product details:

ISBN-10 :  0128045114 

ISBN-13 :  9780128045114

Author:   Victor Kowalenko 

The Partition Method for a Power Series Expansion: Theory and Applications explores how the method known as ‘the partition method for a power series expansion’, which was developed by the author, can be applied to a host of previously intractable problems in mathematics and physics.

In particular, this book describes how the method can be used to determine the Bernoulli, cosecant, and reciprocal logarithm numbers, which appear as the coefficients of the resulting power series expansions, then also extending the method to more complicated situations where the coefficients become polynomials or mathematical functions. From these examples, a general theory for the method is presented, which enables a programming methodology to be established.

The Partition Method for a Power Series Expansion: Theory and Applications 1st Table of contents:

1 Introduction
1.1 Cosecant Expansion
1.2 Reciprocal Logarithm Numbers
1.3 Bernoulli and Related Polynomials
2 More Advanced Applications
2.1 Bell Polynomials of the First Kind
2.2 Generalized Cosecant and Secant Numbers
2.3 Generalized Reciprocal Logarithm Numbers
2.4 Generalization of Elliptic Integrals
3 Generating Partitions
4 General Theory
5 Programming the Partition Method for a Power Series Expansion
6 Operator Approach
7 Classes of Partitions
8 The Partition-Number Generating Function and Its Inverted Form
8.1 Generalization of the Inverted Form of P(z)
9 Generalization of the Partition-Number Generating Function
10 Conclusion

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Tags: The Partition Method, Power Series Expansion, Theory, Applications, Victor Kowalenko