A Dirac delta-type orthogonality relation for the on-the-cut generalized associated Legendre functions of the first kind with imaginary second upper indices

作者：Szmytkowski Radoslaw^*; Bielski Sebastian

来源：Integral Transforms and Special Functions, 2014, 25(4): 312-317.

DOI：10.1080/10652469.2013.842235

• special functions
• generalized associated Legendre functions
• orthogonal functions
• the Dirac delta distribution

The integral integral(1)(-1) dx(1+x)-1P(nu)(lambda,iu)(x)P-nu(lambda,iu)'(x), involving the on-the-cut generalized associated Legendre functions of the first kind with C, Re lambda < 1 or lambda is an element of N+, mu, mu', is an element of R, is evaluated in a closed form. It is found to be proportional to 2(i mu/2)delta(mu - mu') + 2(-i /2)delta(mu + mu), where delta(mu -/+ mu') is the Dirac delta distribution.

• 出版日期2014-4-3