روش تقسیم برای گسترش سری توانی: نظریه و کاربردها

__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. Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics. * Explains the partition method by presenting elementary applications involving the Bernoulli, cosecant, and reciprocal logarithm numbers * Compares generating partitions via the BRCP algorithm with the standard lexicographic approaches * Describes how to program the partition method for a power series expansion and the BRCP algorithm

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.

Finally, the programming techniques of previous chapters are used to derive power series expansions for complex generating functions arising in the theory of partitions and in lattice models of statistical mechanics.

• Explains the partition method by presenting elementary applications involving the Bernoulli, cosecant, and reciprocal logarithm numbers
• Compares generating partitions via the BRCP algorithm with the standard lexicographic approaches
• Describes how to program the partition method for a power series expansion and the BRCP algorithm

Front Cover -- The Partition Method for a Power Series Expansion -- Copyright -- Contents -- Preface -- 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 -- A Regularization -- B Computer Programs -- References -- Index -- Back Cover Content: Front Cover The Partition Method for a Power Series Expansion Copyright Contents Preface 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 Form8.1 Generalization of the Inverted Form of P(z) 9 Generalization of the Partition-Number Generating Function 10 Conclusion A Regularization B Computer Programs References Index Back Cover.