Bessel, Friedrich Wilhelm

Bessel. Friedrich Wilhelm (1784-1846) German astronomer. As an unqualified amateur he catalogued the positions of50 000 stars and calculated the distance to 61 Cygni from its parallax. In 1844 he discovered that Sirius is a binary star with a dark companion. Solving the complex mathematics in these studies led him to develop Bessel functions. 

Berzelius Jons Jacob Baron (1779-1848) Swed. chem., founder of modern chemistry ( Theory of Chemical Proportions 1814), oxygen as the standard for atomic weights, pioneered gravimetric analysis Bessel Friedrich Wilhelm (1784-1864),... 

Acknowledgments We would like to thank the National Science Foundation (DMR-0135233, DMR-0703988, Chem-0456719, Chem-0723497), the ACS Petroleum Research Fund (36730-G7), the Dupont Company, the 3 M Company, the Simitomo Company, the Rhom and Haas Company, and the Univesity of California at Irvine for generous financial support. ZG gratefully acknowledges a Friedrich Wilhelm Bessel Research Award granted by the Alexander von Humboldt Foundation, a National Science Foundation CAREER Award, and a Camille Dreyfus Teacher-Scholar Award. CSP acknowledges an Allergan Fellowship, a UCI dissertation fellowship, and the Joan Rowland award from UCI. 

We hasten to add that we have introduced even more Bessel functions neither for completeness nor for the further aggrandizement of Friedrich Wilhelm Bessel (1784-1846), who, with a veritable zoo of functions to his credit, not to mention infinite series, a revered inequality, an interpolation scheme, and various other mathematical artifacts, needs no publicity as we shall see, (4.13) and (4.14) will save some labor, a sufficient reason for admitting more functions into our larder. 

I. L. F. is grateful to the Alexander von Humboldt Foundation for the Friedrich Wilhelm Bessel Award, who made it possible to work on this part of EIC II during the stay at TU Berlin in 2003. 

Friedrich Wilhelm Bessel, bom Jul. 22, 1784, in Minden, Germany, died Mtir. 17, 1846, in Kdnigsberg, now Russia. 

Bessel function A type of function that occurs as a solution to problems involving waves in systems with cylindrical symmetry. Bessel functions have b n extensively studied and tabulated and are used in many branches of mathematical physics. They are named after the German astronomer Friedrich Wilhelm Bessel (1784-1846). 

The author is indebted to Professors H. Koppel and L. S. Cederbaum for their interest in this work and a fruitful collaboration which resulted in the first publication (Ref. 30) on this subject. Thanks are due to Professors W. Domcke and H. Koppel for their kind invitation and encouragement to contribute this chapter in the present book. This study is supported in part by a grant from the department of science and technology, New Delhi under the fast track scheme. S. M. is a receipient of the Friedrich Wilhelm Bessel Forschungspreis of the Alexander von Humboldt Stiftung. 

In 1991, he was Senior Researcher at the Laboratory of Theory and Modeling of Polymers, Institute of Macromolecular Compounds of the Russian Academy of Sciences, St. Petersburg, Russia and in 2007, he worked as Research Director at CNRS, Institut Pluridisdplinaire de Recherche sur I Environnement et les Materiaux, Pau, France. He has received the Alexander von Humboldt Fellowship (1994) and Friedrich Wilhelm Bessel Research Award (2004). 

The general solution is h cor)=AC cor )t- BS(a>r) where A and B are constants of integration. The solutions form an infinite series and are listed in tables and plotted. They are used in the study of fluid mechanics and heat transfer, and named after German astronomer Friedrich Wilhelm Bessel (1784-1846). 

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