Bessel functions have the peculiarity of being functions of two independent variables: argument and order. They have been studied extensively because of their countless applications, but the vast majority of available literature is devoted to the case of fixed order, variable argument. This two-volume work explores the opposite case. This volume focuses on properties of the functions and mathematical operations with respect to the order.

Bessel functions have the peculiarity of being functions of two independent variables: argument and order. They have been studied extensively because of their countless applications, but the vast majority of available literature is devoted to the case of fixed order, variable argument. This two-volume work explores the opposite case. This volume collects tabulations of the first, second, and third derivatives with respect to the order.

This monograph is devoted to different aspects associated with citric acid, inorganic citrates and their aqueous and organic solutions. It includes information about properties, occurrence and technological applications of citric acid and inorganic citrates. Phase equilibria - melting, freezing, boiling, vapour pressures, solubilities of citric acid in water, organic solvents and ternary systems are presented, correlated, and analyzed. Dynamic properties - viscosities, diffusion coefficients, electrical conductivities and surface tensions are examined. Mathematical representations of citric acid dissociation, in electrolyte solutions and in buffers are discussed. Citric acid chemistry - syntheses of citric acid, neutralization, degradation, oxidation, esterification, formation of anhydrides, amides and citrate-based siderophores is reviewed.

The Volterra functions appeared at the beginning of the second decade of the twentieth century in the theory of definite integrals, integral equations and prime numbers in the works of famous mathematicians Srinivasa Ramanujan, Jacques Touchard, Vito Volterra and Edmund Landau. However, between 1943-1953, the Volterra functions started to play an important role also in the investigations of a number of French mathematicians because they found that these functions are the direct and inverse transforms in the laplace transformation of some elementary and special functions. This book examines both integral equations and Volterra functions in detail and highlights the important roles that each of these functions perform.

This book will serve as a reference book that contains a comprehensive list of formulas for the first time, tables of the Volterra functions. It also includes critically evaluated older material on the functions, but many new results that were obtained by the author. These results include: the behaviour of the Volterra Functions as a function of parameters, the integral representations of the functions, many new Laplace and other-one-dimensional and two-dimensional integral transforms, integrals and series as well as extensive numerical computations that are presented in graphical and tabular forms.