베셀 함수

개요

• 베셀 함수
• 제1종 변형 베셀 함수
• 제2종 변형 베셀함수

\[ K_{\nu }(x)= \int_0^{\infty } (\exp (-x (\cosh t))) (\cosh (\nu t)) \, dt \]

메모

• http://mathoverflow.net/questions/105971/how-should-an-analytic-number-theorist-look-at-bessel-functions
• NIST Digital Library of Mathematical Functions

관련된 항목들

• 분할수의 근사 공식 (하디-라마누잔-라데마커 공식)
• 타원 모듈라 j-함수 (elliptic modular function, j-invariant)

관련논문

• Zhi Qi, Theory of Bessel Functions of High Rank - II: Hankel Transforms and Fundamental Bessel Kernels, arXiv:1411.6710 [math.NT], November 25 2014, http://arxiv.org/abs/1411.6710
• Zhi Qi, Theory of Bessel Functions of High Rank - I: Fundamental Bessel Functions, arXiv:1408.5652 [math.NT], August 25 2014, http://arxiv.org/abs/1408.5652
• Zhi Qi, On the Fourier Transform of Bessel Functions over Complex Numbers - I: the Spherical Case, arXiv:1606.02913 [math.CA], June 09 2016, http://arxiv.org/abs/1606.02913
• Maier, Robert S. “Integrals of Lipschitz-Hankel Type, Legendre Functions, and Table Errata.” arXiv:1509.08963 [math], September 29, 2015. http://arxiv.org/abs/1509.08963.