Coulomb Green's function and an addition formula for the Whittaker functions

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21340%2F24%3A00374605" target="_blank" >RIV/68407700:21340/24:00374605 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1063/5.0184924" target="_blank" >https://doi.org/10.1063/5.0184924</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1063/5.0184924" target="_blank" >10.1063/5.0184924</a>

Result language
angličtina
Original language name
Coulomb Green's function and an addition formula for the Whittaker functions
Original language description
A series of the form Sigma(infinity)(l=0) c(k, l)M-k,M-l+1/2(r(0))W-k,W-l+1/2(r)P-l(cos(gamma)) is evaluated explicitly where c(kappa, l) are suitable complex coefficients, M-kappa,M-mu and W-kappa,W-mu are the Whittaker functions, P-l are the Legendre polynomials, r(0) < r are radial variables, gamma is an angle and kappa is a complex parameter. The sum depends, as far as the radial variables and the angle are concerned, on their combinations r + r(0) and (r(2) + r(0)(2) - 2rr(0) cos(gamma))(1/2). This addition formula generalizes in some respect Gegenbauer's Addition Theorem and follows rather straightforwardly from some already known results, particularly from Hostler's formula for Coulomb Green's function. In addition, several complementary summation formulas are derived. They suggest that a further extension of this addition formula may be possible.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10102 - Applied mathematics

Project
<a href="/en/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Center for advanced applied science</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2024
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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