Jolley L.B.W. Summation of Series

Издательство Dover Publications, 1961, -277 pp.FOR a long time past there has been a need for a collection of series into one small volume for easy reference together with a bibliography indicating at least one of the textbooks to which
reference could be made in case of doubt as to accuracy or to the method by which the series was arrived at.
The 700-odd series in this collection (with the exception of a few which have been specially prepared) are not new, and represent only the labour of extracting the material from the many textbooks on algebra, trigonometry, calculus and the like. Yet such a collection will, it is felt, be of considerable benefit to those engaged in the solution of technical problems, and Will save a great deal of time in searching for the required result.
Criticism may be offered on the grounds that the inclusion of easy algebraical summations is unnecessary, but they have been inserted for a very definite purpose. For example, a series of inverse products may have for its sum an expression which is simple to find; but on the other hand, the solution may entail a complicated expression involving the integration or differentiation of other series. For this reason the arrangement of the series has been difficult, and overlapping is unavoidable in certain instances. To overcome this difficulty, the series have been set forth in as pictorial a manner as possible, so that the form of the individual terms can be readily seen.
On this account also, the inclusion of such series as are evolved for elliptic integrals, Bessel functions and the like has been restricted, perhaps to too great an extent; but reference to standard works is usually essential in such cases, and practically only such references are included.
The final column refers to the bibliography at the beginning of the book, and here again it has been quite impossible for obvious reasons to provide for all the references.Arithmetical Progression
Geometrical Progression
Arithmetical and Geometrical Progression
Powers of Natural Numbers
Products of Natural Numbers
Figurate and Polygonal Numbers
Inverse Natural Numbers
Exponential and Logarithmic Series
Binomials
Simple Inverse Products
Other Inverse Products
Simple Factorials
Other Power Series (Bernoulli's and Euler's Numbers)
Trigonometrical Summations
Hyperbolic Summations
Trigonometrical Expansions
Hyperbolic Expansions
Taylor's and Maclaurin's Theorem
Bessel Functions
Elliptic Functions
Various Integrals
Beta and Gamma Functions
Infinite Products
Fourier's Series
Hypergeometric Functions
Relations Between Products and Series
Special Functions
Zeta Functions
Legendre Polynomials
Special Products
General Forms
Double and Treble Series
Bernoulli's Functions
Bernoulli's Numbers
Table of Bernoulli's Numbers in Vulgar Fractions
Table of Bernoulli's Numbers in Integers and Repeating Decimals
Values of Constants in Series (305) to (318) and (1130)
Euler's Numbers
Euler's Constant
Sum of Power Series
Relations between Bernoulli's Numbers