3 citations · 7 across the 5 of their papers we have counts for
6 papers
Some differentiation formulas for Legendre polynomials
Radoslaw Szmytkowski
In a series of recent works, we have provided a number of explicit expressions for the derivative of the associated Legendre function of the first kind with respect to its degree,…
On parameter derivatives of the associated Legendre function of the first kind (with applications to the construction of the associated Legendre function of the second kind of integer degree and order)
Radoslaw Szmytkowski
A relationship between partial derivatives of the associated Legendre function of the first kind with respect to its degree, , and to its ord…
An orthogonality relation for the Whittaker functions of the second kind of imaginary order
Radoslaw Szmytkowski, Sebastian Bielski
An orthogonality relation for the Whittaker functions of the second kind of imaginary order, , with , is investigated. The integral $\int_{0}^…
Comment on the orthogonality of the Macdonald functions of imaginary order
Radoslaw Szmytkowski, Sebastian Bielski
Recently, Yakubovich [Opuscula Math. 26 (2006) 161--172] and Passian et al. [J. Math. Anal. Appl. doi:10.1016/j.jmaa.2009.06.067] have presented alternative proofs of an orthogonal…
On the derivative of the associated Legendre function of the first kind of integer degree with respect to its order
Radoslaw Szmytkowski
The derivative of the associated Legendre function of the first kind of integer degree with respect to its order, , is studied. After deriving and in…
Addendum to "The Dirac-Coulomb Sturmians and the series expansion of the Dirac-Coulomb Green function: application to the relativistic polarizability of the hydrogen-like atom" [J. Phys. B: At. Mol. Opt. Phys. 30 (1997) 825-61, (E) 30 (1997) 2747]
Radoslaw Szmytkowski
Closure relations satisfied by the radial Dirac-Coulomb Sturmians are proved analytically. The Sturmian expansion of the Dirac-Coulomb Green function is transformed to the form con…