Spheroidal Wave Functions - 30.3 Eigenvalues

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
30.3#Ex4	${\displaystyle{\displaystyle\alpha_{k}=\gamma^{2}\frac{(k+2m+1)(k+2m+2)}{(2k+2m+3)(2k+2m+5)}}}$ \alpha_{k} = \gamma^{2}\frac{(k+2m+1)(k+2m+2)}{(2k+2m+3)(2k+2m+5)}		alpha[k] = (gamma)^(2)*((k + 2*m + 1)*(k + 2*m + 2))/((2*k + 2*m + 3)*(2*k + 2*m + 5))	Subscript[\[Alpha], k] == \[Gamma]^(2)*Divide[(k + 2*m + 1)*(k + 2*m + 2),(2*k + 2*m + 3)*(2*k + 2*m + 5)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.3#Ex5	${\displaystyle{\displaystyle\beta_{k}=(k+m)(k+m+1)-2\gamma^{2}\frac{(k+m)(k+m+1)-1+m^{2}}{(2k+2m-1)(2k+2m+3)}}}$ \beta_{k} = (k+m)(k+m+1)-2\gamma^{2}\frac{(k+m)(k+m+1)-1+m^{2}}{(2k+2m-1)(2k+2m+3)}		beta[k] = (k + m)*(k + m + 1)- 2*(gamma)^(2)*((k + m)*(k + m + 1)- 1 + (m)^(2))/((2*k + 2*m - 1)*(2*k + 2*m + 3))	Subscript[\[Beta], k] == (k + m)*(k + m + 1)- 2*\[Gamma]^(2)*Divide[(k + m)*(k + m + 1)- 1 + (m)^(2),(2*k + 2*m - 1)*(2*k + 2*m + 3)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.3#Ex6	${\displaystyle{\displaystyle\gamma_{k}=\gamma^{2}\frac{(k-1)k}{(2k+2m-3)(2k+2m-1)}}}$ \gamma_{k} = \gamma^{2}\frac{(k-1)k}{(2k+2m-3)(2k+2m-1)}		((gamma)^(2)) = (gamma)^(2)*((k - 1)*k)/((2*k + 2*m - 3)*(2*k + 2*m - 1))	(\[Gamma]^(2)) == \[Gamma]^(2)*Divide[(k - 1)*k,(2*k + 2*m - 3)*(2*k + 2*m - 1)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.3#Ex7	${\displaystyle{\displaystyle\ell_{0}=n(n+1)}}$ \ell_{0} = n(n+1)		ell[0] = n*(n + 1)	Subscript[\[ScriptL], 0] == n*(n + 1)	Skipped - no semantic math	Skipped - no semantic math	-	-
30.3#Ex8	${\displaystyle{\displaystyle 2\ell_{2}=-1-\frac{(2m-1)(2m+1)}{(2n-1)(2n+3)}}}$ 2\ell_{2} = -1-\frac{(2m-1)(2m+1)}{(2n-1)(2n+3)}		2*ell[2] = - 1 -((2*m - 1)*(2*m + 1))/((2*n - 1)*(2*n + 3))	2*Subscript[\[ScriptL], 2] == - 1 -Divide[(2*m - 1)*(2*m + 1),(2*n - 1)*(2*n + 3)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.3#Ex9	${\displaystyle{\displaystyle 2\ell_{4}=\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-3)(2n-1)^{3}(2n+1)}-\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n+1)(2n+3)^{3}(2n+5)}}}$ 2\ell_{4} = \frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-3)(2n-1)^{3}(2n+1)}-\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n+1)(2n+3)^{3}(2n+5)}		2*ell[4] = ((n - m - 1)*(n - m)*(n + m - 1)*(n + m))/((2*n - 3)*(2*n - 1)^(3)*(2*n + 1))-((n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2))/((2*n + 1)*(2*n + 3)^(3)*(2*n + 5))	2*Subscript[\[ScriptL], 4] == Divide[(n - m - 1)*(n - m)*(n + m - 1)*(n + m),(2*n - 3)*(2*n - 1)^(3)*(2*n + 1)]-Divide[(n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2),(2*n + 1)*(2*n + 3)^(3)*(2*n + 5)]	Skipped - no semantic math	Skipped - no semantic math	-	-
30.3.E10	${\displaystyle{\displaystyle\ell_{6}=(4m^{2}-1)\left(\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n-1)(2n+1)(2n+3)^{5}(2n+5)(2n+7)}-\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-5)(2n-3)(2n-1)^{5}(2n+1)(2n+3)}\right)}}$ \ell_{6} = (4m^{2}-1)\left(\frac{(n-m+1)(n-m+2)(n+m+1)(n+m+2)}{(2n-1)(2n+1)(2n+3)^{5}(2n+5)(2n+7)}-\frac{(n-m-1)(n-m)(n+m-1)(n+m)}{(2n-5)(2n-3)(2n-1)^{5}(2n+1)(2n+3)}\right)		ell[6] = (4*(m)^(2)- 1)*(((n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2))/((2*n - 1)*(2*n + 1)*(2*n + 3)^(5)*(2*n + 5)*(2*n + 7))-((n - m - 1)*(n - m)*(n + m - 1)*(n + m))/((2*n - 5)*(2*n - 3)*(2*n - 1)^(5)*(2*n + 1)*(2*n + 3)))	Subscript[\[ScriptL], 6] == (4*(m)^(2)- 1)*(Divide[(n - m + 1)*(n - m + 2)*(n + m + 1)*(n + m + 2),(2*n - 1)*(2*n + 1)*(2*n + 3)^(5)*(2*n + 5)*(2*n + 7)]-Divide[(n - m - 1)*(n - m)*(n + m - 1)*(n + m),(2*n - 5)*(2*n - 3)*(2*n - 1)^(5)*(2*n + 1)*(2*n + 3)])	Skipped - no semantic math	Skipped - no semantic math	-	-
30.3.E11	${\displaystyle{\displaystyle\ell_{8}=2(4m^{2}-1)^{2}A+\frac{1}{16}B+\frac{1}{8}C+\frac{1}{2}D}}$ \ell_{8} = 2(4m^{2}-1)^{2}A+\frac{1}{16}B+\frac{1}{8}C+\frac{1}{2}D		ell[8] = 2*(4*(m)^(2)- 1)^(2)* A +(1)/(16)*B +(1)/(8)*C +(1)/(2)*(((n - m - 1)*(n - m)*(n - m + 1)*(n - m + 2)*(n + m - 1)*(n + m)*(n + m + 1)*(n + m + 2))/((2*n - 3)*(2*n - 1)^(4)*(2*n + 1)^(2)*(2*n + 3)^(4)*(2*n + 5)))	Subscript[\[ScriptL], 8] == 2*(4*(m)^(2)- 1)^(2)* A +Divide[1,16]*B +Divide[1,8]*C +Divide[1,2]*(Divide[(n - m - 1)*(n - m)*(n - m + 1)*(n - m + 2)*(n + m - 1)*(n + m)*(n + m + 1)*(n + m + 2),(2*n - 3)*(2*n - 1)^(4)*(2*n + 1)^(2)*(2*n + 3)^(4)*(2*n + 5)])	Skipped - no semantic math	Skipped - no semantic math	-	-