@@ Property / Symbols used @@
+phase of Coulomb functions
@@ Property / Symbols used: phase of Coulomb functions / rank @@
+Normal rank
@@ Property / Symbols used: phase of Coulomb functions / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{\theta_{\NVar{\ell}}}\left(\NVar{\eta},\NVar{\rho% }\right)}}$ 
\Coulombphasetheta{\NVar{\ell}}@{\NVar{\eta}}{\NVar{\rho}}
@@ Property / Symbols used: phase of Coulomb functions / qualifier @@
+xml-id: C33.S2.E9.m2adec
@@ Property / Symbols used @@
+Kummer confluent hypergeometric function
@@ Property / Symbols used: Kummer confluent hypergeometric function / rank @@
+Normal rank
@@ Property / Symbols used: Kummer confluent hypergeometric function / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$ 
\KummerconfhyperU@{\NVar{a}}{\NVar{b}}{\NVar{z}}
@@ Property / Symbols used: Kummer confluent hypergeometric function / qualifier @@
+xml-id: C13.S2.E6.m2adec
@@ Property / Symbols used @@
+base of natural logarithm
@@ Property / Symbols used: base of natural logarithm / rank @@
+Normal rank
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{e}}}$ 
\expe
@@ Property / Symbols used: base of natural logarithm / qualifier @@
+xml-id: C4.S2.E11.m2addec
@@ Property / Symbols used @@
+imaginary unit
@@ Property / Symbols used: imaginary unit / rank @@
+Normal rank
@@ Property / Symbols used: imaginary unit / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\mathrm{i}}}$ 
\iunit
@@ Property / Symbols used: imaginary unit / qualifier @@
+xml-id: C1.S9.E1.m2addec
@@ Property / Symbols used @@
+irregular Coulomb radial functions
@@ Property / Symbols used: irregular Coulomb radial functions / rank @@
+Normal rank
@@ Property / Symbols used: irregular Coulomb radial functions / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle{H^{\NVar{\pm}}_{\NVar{\ell}}}\left(\NVar{\eta},% \NVar{\rho}\right)}}$ 
\irregCoulombH{\NVar{\pm}}{\NVar{\ell}}@{\NVar{\eta}}{\NVar{\rho}}
@@ Property / Symbols used: irregular Coulomb radial functions / qualifier @@
+xml-id: C33.S2.E7.m2aadec
@@ Property / Symbols used @@
+Q12666
@@ Property / Symbols used: Q12666 / rank @@
+Normal rank
@@ Property / Symbols used: Q12666 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\ell}}$ 
\ell
@@ Property / Symbols used: Q12666 / qualifier @@
+xml-id: C33.S1.XMD2.m1gdec
@@ Property / Symbols used @@
+Q12667
@@ Property / Symbols used: Q12667 / rank @@
+Normal rank
@@ Property / Symbols used: Q12667 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\rho}}$ 
\rho
@@ Property / Symbols used: Q12667 / qualifier @@
+xml-id: C33.S1.XMD5.m1ddec
@@ Property / Symbols used @@
+Q12668
@@ Property / Symbols used: Q12668 / rank @@
+Normal rank
@@ Property / Symbols used: Q12668 / qualifier @@
+Defining formula:  ${\displaystyle{\displaystyle\eta}}$ 
\eta
@@ Property / Symbols used: Q12668 / qualifier @@
+xml-id: C33.S1.XMD7.m1gdec

DLMF:33.2.E8 (Q9503): Difference between revisions

θ ℓ ⁡ ( η , ρ ) Coulomb-phase ℓ 𝜂 𝜌 {\displaystyle{\displaystyle{\theta_{\NVar{\ell}}}\left(\NVar{\eta},\NVar{\rho% }\right)}}

U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}

e {\displaystyle{\displaystyle\mathrm{e}}}

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

H ℓ ± ⁡ ( η , ρ ) irregular-Coulomb-H plus-or-minus ℓ 𝜂 𝜌 {\displaystyle{\displaystyle{H^{\NVar{\pm}}_{\NVar{\ell}}}\left(\NVar{\eta},% \NVar{\rho}\right)}}

ℓ ℓ {\displaystyle{\displaystyle\ell}}

ρ 𝜌 {\displaystyle{\displaystyle\rho}}

η 𝜂 {\displaystyle{\displaystyle\eta}}

Latest revision as of 14:21, 2 January 2020

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${\displaystyle{\displaystyle{\theta_{\NVar{\ell}}}\left(\NVar{\eta},\NVar{\rho% }\right)}}$

${\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}$

${\displaystyle{\displaystyle\mathrm{e}}}$

${\displaystyle{\displaystyle\mathrm{i}}}$

${\displaystyle{\displaystyle{H^{\NVar{\pm}}_{\NVar{\ell}}}\left(\NVar{\eta},% \NVar{\rho}\right)}}$

${\displaystyle{\displaystyle\ell}}$

${\displaystyle{\displaystyle\rho}}$

${\displaystyle{\displaystyle\eta}}$