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

Kód výsledku v 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>

Výsledek na webu

<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>

Jazyk výsledku

angličtina

Název v původním jazyce

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

Popis výsledku v původním jazyce

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.

Název v anglickém jazyce

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

Popis výsledku anglicky

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.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10102 - Applied mathematics

Projekt

<a href="/cs/project/EF16_019%2F0000778" target="_blank" >EF16_019/0000778: Centrum pokročilých aplikovaných přírodních věd</a><br>

Návaznosti

P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Rok uplatnění

2024

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

Journal of Mathematical Physics

ISSN

0022-2488

e-ISSN

1089-7658

Svazek periodika

65

Číslo periodika v rámci svazku

2

Stát vydavatele periodika

US - Spojené státy americké

Počet stran výsledku

15

Strana od-do

1-15

Kód UT WoS článku

001177609700004

EID výsledku v databázi Scopus

2-s2.0-85186385327