On certain new connections between Legendre and Bessel Functions
نویسندگان
چکیده
منابع مشابه
Certain geometric properties of normalized Bessel functions
In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t In this paper, we give a set of sufficient conditions for the normalized form of the generalized Bessel func...
متن کاملA New Take on Spherical, Whittaker and Bessel Functions
0. Introduction 5 0.1. Objectives and main results 5 0.1.1. Affine Satake isomorphisms 5 0.1.2. Whittaker functions 6 0.1.3. The setting of the paper 7 0.2. Dunkl operators via DAHA 7 0.2.1. Families of Dunkl operators 8 0.3. The technique of spinors 9 0.3.1. Connections to AKZ 9 0.3.2. Isomorphism theorems 10 0.3.3. The localization functor 10 0.3.4. The Whittaker limit 11 0.4. On Langlands’ p...
متن کاملThe BLT (Bessel-Legendre-Trigonometric) System
Note that all the numerators in the argument of the arctan functions are positive by definition, so that the arguments take on values (−∞,+∞), corresponding to which the computed angles take values θi ∈ [0, π] for i = 1, · · · , D−2, just as needed. This succession would imply the assignment θD−1 = arctan( x 1 x2 ) for the 1 See for more info, in a sli...
متن کاملOn A Certain Class of Bessel Integrals
There are many old results of integrals involving Bessel functions, currently available in handbooks, but we found no recourse in the well-known references to how they were established. In this paper, we attempt to have a clear way of proving some of these results . In fact, we consider a certain class of Bessel integrals where we prove that such integrals vanish under certain conditions. To th...
متن کاملEvaluation of Certain Legendre Symbols
We state and prove an apparently hitherto unrecorded evaluation of certain Legendre symbols: if p is prime, p 6= 2, and ab = p − 1, then the Legendre symbol ( b p ) is given by ( b p ) = (−1).
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1935
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500008099