03999nam 22011295 450 991015474650332120190708092533.01-4008-8237-010.1515/9781400882373(CKB)3710000000628068(MiAaPQ)EBC4738712(DE-B1597)468023(OCoLC)979836553(DE-B1597)9781400882373(EXLCZ)99371000000062806820190708d2016 fg engurcnu||||||||rdacontentrdamediardacarrierAn Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18 /Clifford TruesdellPrinceton, NJ : Princeton University Press, [2016]©19491 online resource (197 pages) illustrationsAnnals of Mathematics Studies ;3480-691-09577-9 Bibliography.PREFACE -- TABLE OF CONTENTS -- Chapter I. The Object and Plan of This Essay -- Chapter II. Reduction to The F-Equation -- Chapter III. Existence and Uniqueness Theorems -- Chapter IV. Methods of Treating Special Functions Based on The Uniqueness Theorem for The Condition F(z, αO) = ψ (z) -- Chapter V. Remarks on Solutions Such That F(z, αO) = ψ (z) -- Chapter VI. Conclusions and Unsolved Problems -- Appendix I. Special Functions -- Appendix II. Operators -- Appendix III. Examples of Equations of Type (3-4) Not Reducible to The F-Equation -- BibliographyThe description for this book, An Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 18, will be forthcoming.Annals of mathematics studies ;no. 18.Functional equationsAddition.Antiderivative.Asymptotic formula.Bessel function.Beta function.Boundary value problem.Change of variables.Closed-form expression.Coefficient.Combination.Continuous function.Corollary.Differential equation.Enumeration.Equation.Existential quantification.Explicit formula.Exponential function.Factorial.Function (mathematics).Functional equation.Hermite polynomials.Hypergeometric function.Integer.Laguerre polynomials.Laplace transform.Legendre function.Linear difference equation.Linear differential equation.Mathematical induction.Mathematician.Monomial.Natural number.Number theory.Ordinary differential equation.Parameter.Periodic function.Polygamma function.Polynomial.Potential theory.Power series.Rectangle.Recurrence relation.Remainder.Scientific notation.Sequent.Simple function.Singular solution.Special case.Special functions.Summation.Theorem.Theory.Uniqueness theorem.Variable (mathematics).Without loss of generality.Functional equations.517.5Truesdell Clifford, 17725DE-B1597DE-B1597BOOK9910154746503321An Essay Toward a Unified Theory of Special Functions. (AM-18), Volume 182785797UNINA