Coulomb Functions - 33.22 Particle Scattering and Atomic and Molecular Spectra

From testwiki
Revision as of 13:14, 28 June 2021 by Admin (talk | contribs) (Admin moved page Main Page to Verifying DLMF with Maple and Mathematica)
(diff) ← Older revision | Latest revision (diff) | Newer revision β†’ (diff)
Jump to navigation Jump to search


DLMF Formula Constraints Maple Mathematica Symbolic
Maple 		Symbolic
Mathematica 		Numeric
Maple 		Numeric
Mathematica
33.22.E3 d 2 w d x 2 + ( 𝗄 2 - 2 ⁒ Z x - β„“ ⁒ ( β„“ + 1 ) x 2 ) ⁒ w = 0 derivative 𝑀 π‘₯ 2 superscript 𝗄 2 2 𝑍 π‘₯ β„“ β„“ 1 superscript π‘₯ 2 𝑀 0 {\displaystyle{\displaystyle\frac{{\mathrm{d}}^{2}w}{{\mathrm{d}x}^{2}}+\left(% {\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w=0}}
\deriv[2]{w}{x}+\left({\sf k}^{2}-\frac{2Z}{x}-\frac{\ell(\ell+1)}{x^{2}}\right)w = 0		 

diff(w, [x$(2)])+((k)^(2)-(2*Z)/(x)-(ell*(ell + 1))/((x)^(2)))*w = 0

D[w, {x, 2}]+((k)^(2)-Divide[2*Z,x]-Divide[\[ScriptL]*(\[ScriptL]+ 1),(x)^(2)])*w == 0
Failure Failure Error
Failed [297 / 300]
Result: Complex[-0.5704416218017292, -1.0991449828236957]
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β„“, 1]}


Result: Complex[-2.110042339640732, -1.9880338717125847]
Test Values: {Rule[k, 1], Rule[w, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[x, Rational[3, 2]], Rule[Z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[β„“, 2]}

... skip entries to safe data
33.22#Ex10 r = - Ξ· ⁒ ρ π‘Ÿ πœ‚ 𝜌 {\displaystyle{\displaystyle r=-\eta\rho}}
r = -\eta\rho		 

r = - eta*rho
 
r == - \[Eta]*\[Rho]
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex11 Ο΅ = 1 / Ξ· 2 italic-Ο΅ 1 superscript πœ‚ 2 {\displaystyle{\displaystyle\epsilon=1/\eta^{2}}}
\epsilon = 1/\eta^{2}		 

epsilon = 1/(eta)^(2)
 
\[Epsilon] == 1/\[Eta]^(2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex12 z = 2 ⁒ i ⁒ ρ 𝑧 2 imaginary-unit 𝜌 {\displaystyle{\displaystyle z=2\mathrm{i}\rho}}
z = 2\iunit\rho		 

z = 2*I*rho

z == 2*I*\[Rho]
Failure Failure
Failed [70 / 70]
Result: 1.866025404-1.232050808*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: .5000000000-.8660254040*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [70 / 70]
Result: Complex[1.8660254037844386, -1.2320508075688774]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[2.598076211353316, 1.4999999999999996]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex13 ΞΊ = i ⁒ Ξ· πœ… imaginary-unit πœ‚ {\displaystyle{\displaystyle\kappa=\mathrm{i}\eta}}
\kappa = \iunit\eta		 

kappa = I*eta

\[Kappa] == I*\[Eta]
Failure Failure
Failed [96 / 100]
Result: 1.366025404-.3660254040*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}


Result: 1.000000000-1.732050808*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}

... skip entries to safe data
Failed [96 / 100]
Result: Complex[1.3660254037844386, -0.36602540378443876]
Test Values: {Rule[Ξ·, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ΞΊ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[1.0, -1.7320508075688772]
Test Values: {Rule[Ξ·, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ΞΊ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex14 ρ = z / ( 2 ⁒ i ) 𝜌 𝑧 2 imaginary-unit {\displaystyle{\displaystyle\rho=z/(2\mathrm{i})}}
\rho = z/(2\iunit)		 

rho = z/(2*I)

\[Rho] == z/(2*I)
Failure Failure
Failed [70 / 70]
Result: .6160254040+.9330127020*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = 1/2*3^(1/2)+1/2*I}


Result: .4330127020+.2500000000*I
Test Values: {rho = 1/2*3^(1/2)+1/2*I, z = -1/2+1/2*I*3^(1/2)}

... skip entries to safe data
Failed [70 / 70]
Result: Complex[0.6160254037844387, 0.9330127018922193]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[-0.7499999999999998, 1.299038105676658]
Test Values: {Rule[z, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ρ, Power[E, Times[Complex[0, Rational[2, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex15 Ξ· = ΞΊ / i πœ‚ πœ… imaginary-unit {\displaystyle{\displaystyle\eta=\kappa/\mathrm{i}}}
\eta = \kappa/\iunit		 

eta = kappa/I

\[Eta] == \[Kappa]/I
Failure Failure
Failed [96 / 100]
Result: .3660254040+1.366025404*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2*3^(1/2)+1/2*I}


Result: 1.732050808+1.000000000*I
Test Values: {eta = 1/2*3^(1/2)+1/2*I, kappa = 1/2-1/2*I*3^(1/2)}

... skip entries to safe data
Failed [96 / 100]
Result: Complex[0.36602540378443876, 1.3660254037844386]
Test Values: {Rule[Ξ·, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ΞΊ, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]]}


Result: Complex[1.7320508075688772, 1.0]
Test Values: {Rule[Ξ·, Power[E, Times[Complex[0, Rational[1, 6]], Pi]]], Rule[ΞΊ, Power[E, Times[Complex[0, Rational[-1, 3]], Pi]]]}

... skip entries to safe data
33.22#Ex16 r = ΞΊ ⁒ z / 2 π‘Ÿ πœ… 𝑧 2 {\displaystyle{\displaystyle r=\kappa z/2}}
r = \kappa z/2		 

r = kappa*z/2
 
r == \[Kappa]*z/2
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex17 Ο΅ = - 1 / ΞΊ 2 italic-Ο΅ 1 superscript πœ… 2 {\displaystyle{\displaystyle\epsilon=-1/\kappa^{2}}}
\epsilon = -1/\kappa^{2}		 

epsilon = - 1/(kappa)^(2)
 
\[Epsilon] == - 1/\[Kappa]^(2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex18 Ξ· = + Ο΅ - 1 / 2 πœ‚ superscript italic-Ο΅ 1 2 {\displaystyle{\displaystyle\eta=+\epsilon^{-1/2}}}
\eta = +\epsilon^{-1/2}		 

eta = + (epsilon)^(- 1/2)
 
\[Eta] == + \[Epsilon]^(- 1/2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex19 ρ = - r / Ξ· 𝜌 π‘Ÿ πœ‚ {\displaystyle{\displaystyle\rho=-r/\eta}}
\rho = -r/\eta		 

rho = - r/eta
 
\[Rho] == - r/\[Eta]
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex20 ΞΊ = + ( - Ο΅ ) - 1 / 2 πœ… superscript italic-Ο΅ 1 2 {\displaystyle{\displaystyle\kappa=+(-\epsilon)^{-1/2}}}
\kappa = +(-\epsilon)^{-1/2}		 

kappa = +(- epsilon)^(- 1/2)
 
\[Kappa] == +(- \[Epsilon])^(- 1/2)
 Skipped - no semantic math Skipped - no semantic math - -
33.22#Ex21 z = 2 ⁒ r / ΞΊ 𝑧 2 π‘Ÿ πœ… {\displaystyle{\displaystyle z=2r/\kappa}}
z = 2r/\kappa		 

z = 2*r/kappa
 
z == 2*r/\[Kappa]
 Skipped - no semantic math Skipped - no semantic math - -
Retrieved from "https://lct.wmflabs.org/w/index.php?title=33.22&oldid=58556"