Mathieu Functions and Hill’s Equation - 28.14 Fourier Series

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
28.14.E1	${\displaystyle{\displaystyle\mathrm{me}_{\nu}\left(z,q\right)=\sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\mathrm{i}(\nu+2m)z}}}$ \Mathieume{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)e^{\iunit(\nu+2m)z}		Error	Sqrt[2]*MathieuC[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Exp[I*(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]	Missing Macro Error	Failure	-	Skipped - Because timed out
28.14.E2	${\displaystyle{\displaystyle\mathrm{ce}_{\nu}\left(z,q\right)=\sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\cos(\nu+2m)z}}$ \Mathieuce{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\cos@@{(\nu+2m)z}		MathieuCE(nu, q, z) = sum((c[2*m])^(nu)(q)* cos((nu + 2*m)*z), m = - infinity..infinity)	MathieuC[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Cos[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]	Failure	Failure	Error	Skipped - Because timed out
28.14.E3	${\displaystyle{\displaystyle\mathrm{se}_{\nu}\left(z,q\right)=\sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\sin(\nu+2m)z}}$ \Mathieuse{\nu}@{z}{q} = \sum_{m=-\infty}^{\infty}c^{\nu}_{2m}(q)\sin@@{(\nu+2m)z}		MathieuSE(nu, q, z) = sum((c[2*m])^(nu)(q)* sin((nu + 2*m)*z), m = - infinity..infinity)	MathieuS[\[Nu], q, z] == Sum[(Subscript[c, 2*m])^\[Nu][q]* Sin[(\[Nu]+ 2*m)*z], {m, - Infinity, Infinity}, GenerateConditions->None]	Failure	Failure	Error	Skipped - Because timed out
28.14.E4	${\displaystyle{\displaystyle qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2m-2}=0}}$ qc_{2m+2}-\left(a-(\nu+2m)^{2}\right)c_{2m}+qc_{2m-2} = 0	${\displaystyle{\displaystyle a=\lambda_{\nu}\left(q\right),c_{2m}=c_{2m}^{\nu}(q)}}$	q*c[2*m + 2]-(a -(nu + 2*m)^(2))*c[2*m]+ q*c[2*m - 2] = 0	q*Subscript[c, 2*m + 2]-(a -(\[Nu]+ 2*m)^(2))*Subscript[c, 2*m]+ q*Subscript[c, 2*m - 2] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-
28.14.E5	${\displaystyle{\displaystyle\sum_{m=-\infty}^{\infty}\left(c_{2m}^{\nu}(q)\right)^{2}=1}}$ \sum_{m=-\infty}^{\infty}\left(c_{2m}^{\nu}(q)\right)^{2} = 1		sum(((c[2*m])^(nu)(q))^(2), m = - infinity..infinity) = 1	Sum[((Subscript[c, 2*m])^\[Nu][q])^(2), {m, - Infinity, Infinity}, GenerateConditions->None] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
28.14.E7	${\displaystyle{\displaystyle c_{-2m}^{-\nu}(q)=c_{2m}^{\nu}(q)}}$ c_{-2m}^{-\nu}(q) = c_{2m}^{\nu}(q)		(c[- 2*m])^(- nu)(q) = (c[2*m])^(nu)(q)	(Subscript[c, - 2*m])^(- \[Nu])[q] == (Subscript[c, 2*m])^\[Nu][q]	Skipped - no semantic math	Skipped - no semantic math	-	-
28.14.E8	${\displaystyle{\displaystyle c_{2m}^{\nu}(-q)=(-1)^{m}c_{2m}^{\nu}(q)}}$ c_{2m}^{\nu}(-q) = (-1)^{m}c_{2m}^{\nu}(q)		(c[2*m])^(nu)(- q) = (- 1)^(m)* (c[2*m])^(nu)(q)	(Subscript[c, 2*m])^\[Nu][- q] == (- 1)^(m)* (Subscript[c, 2*m])^\[Nu][q]	Skipped - no semantic math	Skipped - no semantic math	-	-
28.14#Ex1	${\displaystyle{\displaystyle c_{0}^{\nu}(0)=1}}$ c_{0}^{\nu}(0) = 1		(c[0])^(nu)(0) = 1	(Subscript[c, 0])^\[Nu][0] == 1	Skipped - no semantic math	Skipped - no semantic math	-	-
28.14#Ex2	${\displaystyle{\displaystyle c_{2m}^{\nu}(0)=0}}$ c_{2m}^{\nu}(0) = 0	${\displaystyle{\displaystyle m\neq 0}}$	(c[2*m])^(nu)(0) = 0	(Subscript[c, 2*m])^\[Nu][0] == 0	Skipped - no semantic math	Skipped - no semantic math	-	-