To say that this is the best book on the quantum theory of fields is no praise, since to my knowledge it is the only book on this subject But it is a very good and most useful book The original was written in German and appeared in 1942 This is a translation with some minor changes A few remarks have been added, concerning meson theory and nuclear forces, also footnotes referring to modern work in this field, and finally an appendix on the symmetrization of the energy momentum tensor according to Belinfante Quantum Theory of Fields Prof Gregor Wentzel Translated from the German by Charlotte Houtermans and J M Jauch Pp ix + 224, (New York and London: Interscience Publishers, Inc, 1949) 36s

Quantum Theory of Fields

Zeros of orthogonal polynomials

Introduction References and Suggested Readings PART I REAL DYNAMIC MACROECONOMIC MODELS 1. Dynamic Programming A General Intertemporal Problem A Recursive Problem Bellman's Equations Nonstochastic Examples The Optimal Linear Regulator Problem Stochastic Control Problems Examples of Stochastic Control Problems The Stochastic Linear Optimal Regulator Problem Dynamic Programming and Lucas's Critique Dynamic Games and the Time Inconsistency Phenomenon Conclusions Exercises References and Suggested Readings 2. Search Nonnegative Random Variables Stigler's Model of Search Sequential Search for the Lowest Price Mean-Preserving Spreads Increases in Risk and the Reservation Price Intertemporal Job Search Waiting Times Firing Jovanovic's Matching Model Conclusions Exercises References and Suggested Readings 3. Asset Prices and Consumption Hall's Random Walk Theory of Consumption The Random Walk Theory of Stock Prices Lucas's Model of Asset Prices Mehra and Prescott's Finite-State Version of Lucas's Model Asset Pricing More Generally The Modigliani-Miller Theorem Government Debt and the Ricardian Proposition Remarks on Testing and Estimation Conclusions Exercises References and Suggested Readings PART II MONETARY ECONOMICS AND GOVERNMENT FINANCE 4. Currency in the Utility Function The Price of Inconvertible Government Currency in Lucas's Tree Model Issues and Models in Monetary Economics Government Debt in the Utility Function Government Currency in the Utility Function Seignorage and the Optimum Quantity of Currency A Neutrality Proposition Conclusions References and Suggested Readings 5. Cash-in-Advance Models A One-Country Model Fisher Equations Inflation-Indexed Government Debt Interactions of Monetary and Fiscal Policies Interest on Reserves A Two-Country Model Exchange Rate Indeterminacy Conclusions Exercises References and Suggested Readings 6. Credit and Currency with Long-Lived Agents The Physical Setup Optimal Allocations Competitive Equilibrium A Digression on the Balances of Trade and Payments The Ricardian Doctrine about Taxes and Government Debt The Model with Valued Currency and No Private Debt An Interventionist Optimal Monetary Equilibrium Townsend's \"Turnpike\" Interpretation Conclusions Exercises References and Suggested Readings 7. Credit and Currency with Overlapping Generations The Overlapping-Generations Model The Ricardian Doctrine about Taxes and Government Debt Again A Ricardian Proposition Currency, Bonds, and Open-Market Operations Computing Equilibria Interpretations as Currency Equilibria Optimality Four Examples on Inflation and Its Causes Seignorage and the Laffer Curve Dynamics of Seignorage Forced Saving International Exchange Rates Conclusions Exercises References and Suggested Readings 8. Government Finance in Stochastic Overlapping-Generations Models The Economy Some Examples A General Irrelevance Theorem Wallace's Modigliani-Miller Theorem for Open-Market Operations Chamley and Polemarchakis's Neutrality Theorem Interpretation as a Constant Fiscal Policy Indexed Government Bonds A Ricardian Proposition Further Irrelevance Theorems Conclusions Exercises References and Suggested Readings Appendix. Functional Analysis for Macroeconomics Metric Spaces and Operators First-Order Linear Difference Equations A Formula of Hansen and Sargent A Quadratic Optimization Problem in R A Discounted Quadratic Optimization Problem Predicting a Geometric Distributed Lead of a Stochastic Process Discounted Dynamic Programming A Search Problem Exercises References and Suggested Readings Index

Dynamic Macroeconomic Theory

Lie Theory and Special Functions

Special functions for engineers and applied mathematicians

Hermite-based Appell polynomials: Properties and applications

Laguerre-based Appell polynomials: Properties and applications

Implicit summation formulae for Hermite and related polynomials

The Glaisher rule is an operational identity involving the action of an exponential operator containing the second-order derivatives acting on an exponential function. We use the Crofton and monomiality formalism to derive generalized forms to the multi-dimensional case and show its usefulness in the derivation of old and new forms of generating functions for a wealth of Hermite polynomials families.

On Crofton–Glaisher type relations and derivation of generating functions for Hermite polynomials including the multi-index case

A general class of the 2-variable polynomials is considered, and its properties are derived. Further, these polynomials are used to introduce the 2-variable general-Appell polynomials (2VgAP). The generating function for the 2VgAP is derived, and a correspondence between these polynomials and the Appell polynomials is established. The differential equation, recurrence relations, and other properties for the 2VgAP are obtained within the context of the monomiality principle. This paper is the first attempt in the direction of introducing a new family of special polynomials, which includes many other new special polynomial families as its particular cases.

/pdf/general-appell-polynomials-within-the-context-of-monomiality-4za01ly68p.pdf

Subuhi Khan

Papers

Hermite-based Appell polynomials: Properties and applications

Laguerre-based Appell polynomials: Properties and applications

Implicit summation formulae for Hermite and related polynomials

On Crofton–Glaisher type relations and derivation of generating functions for Hermite polynomials including the multi-index case

General-Appell Polynomials within the Context of Monomiality Principle