Mathieu Functions and Hill’s Equation - 28.7 Analytic Continuation of Eigenvalues

DLMF	Formula	Constraints	Maple	Mathematica	Symbolic Maple	Symbolic Mathematica	Numeric Maple	Numeric Mathematica
28.7.E1	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(a_{2n}\left(q\right)-(2n)^{2}\right)=0}}$ \sum_{n=0}^{\infty}\left(\Mathieueigvala{2n}@{q}-(2n)^{2}\right) = 0		sum(MathieuA(2*n, q)-(2*n)^(2), n = 0..infinity) = 0	Sum[MathieuCharacteristicA[2*n, q]-(2*n)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
28.7.E2	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(a_{2n+1}\left(q\right)-(2n+1)^{2}\right)=q}}$ \sum_{n=0}^{\infty}\left(\Mathieueigvala{2n+1}@{q}-(2n+1)^{2}\right) = q		sum(MathieuA(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = q	Sum[MathieuCharacteristicA[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == q	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
28.7.E3	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(b_{2n+1}\left(q\right)-(2n+1)^{2}\right)=-q}}$ \sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+1}@{q}-(2n+1)^{2}\right) = -q		sum(MathieuB(2*n + 1, q)-(2*n + 1)^(2), n = 0..infinity) = - q	Sum[MathieuCharacteristicB[2*n + 1, q]-(2*n + 1)^(2), {n, 0, Infinity}, GenerateConditions->None] == - q	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out
28.7.E4	${\displaystyle{\displaystyle\sum_{n=0}^{\infty}\left(b_{2n+2}\left(q\right)-(2n+2)^{2}\right)=0}}$ \sum_{n=0}^{\infty}\left(\Mathieueigvalb{2n+2}@{q}-(2n+2)^{2}\right) = 0		sum(MathieuB(2*n + 2, q)-(2*n + 2)^(2), n = 0..infinity) = 0	Sum[MathieuCharacteristicB[2*n + 2, q]-(2*n + 2)^(2), {n, 0, Infinity}, GenerateConditions->None] == 0	Failure	Failure	Skipped - Because timed out	Skipped - Because timed out