Integer Order Characteristic Values

Mathieu.a — Function

a(m,q)

Compute the characteristic value $a_m(q)$ corresponding to an even (cosine-elliptic) solution to the angular Mathieu equation. m is the order of the solution and must be an integer $m=0,1,2,3…$.

Pass a vector, e.g. m=0:4, to compute multiple characteristic values efficiently.

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Mathieu.aa — Function

aa(n,q)

Compute the characteristic value $a_{2n+1}(q)$ corresponding to an even (cosine-elliptic), π-antiperiodic (2π-periodic) solution to the angular Mathieu equation, for $n=0,1,2,3,…$.

Pass a vector, e.g. n=0:4, to compute multiple characteristic values efficiently.

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Mathieu.ap — Function

ap(n,q)

Compute the characteristic value $a_{2n}(q)$ corresponding to an even (cosine-elliptic), π-periodic solution to the angular Mathieu equation, for $n=0,1,2,3,…$.

Pass a vector, e.g. n=0:4, to compute multiple characteristic values efficiently.

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Mathieu.b — Function

b(m,q)

Compute the characteristic value $b_m(q)$ corresponding to an odd (sine-elliptic) solution to the angular Mathieu equation. m is the order of the solution and must be an integer, excluding 0, $m=1,2,3,4…$.

Pass a vector, e.g. m=1:5, to compute multiple characteristic values efficiently.

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Mathieu.ba — Function

ba(n,q)

Compute the characteristic value $b_{2n+1}(q)$ corresponding to an odd (sine-elliptic), π-antiperiodic (2π-periodic) solution to the angular Mathieu equation, for $n=0,1,2,3,…$.

Pass a vector, e.g. n=0:4, to compute multiple characteristic values efficiently.

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Mathieu.bp — Function

bp(n,q)

Compute the characteristic value $b_{2n+2}(q)$ corresponding to an odd (sine-elliptic), π-periodic solution to the angular Mathieu equation, for $n=0,1,2,3,…$.

Pass a vector, e.g. n=0:4, to compute multiple characteristic values efficiently.

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Mathieu.char_aper — Function

char_aper(m,q)

Compute the characteristic value $a_{m+1}(q)$ for even m, or $b_{m}(q)$ for odd m. These characteristic values correspond respectively to even and odd π-antiperiodic (2π-periodic) solutions to the angular Mathieu equation, for $n=0,1,2,3,…$.

m	value
0	a_1
1	b_1
2	a_3
3	b_3
4	a_5
⋮	⋮

Pass a vector, e.g. m=0:4, to compute multiple characteristic values efficiently.

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Mathieu.char_per — Function

char_per(m,q)

Compute the characteristic value $a_{m}(q)$ for even m, or $b_{m+1}(q)$ for odd m. These characteristic values correspond respectively to even and odd π-periodic solutions to the angular Mathieu equation, for $n=0,1,2,3,…$.

m	value
0	a_0
1	b_2
2	a_2
3	b_4
4	a_4
⋮	⋮

Pass a vector, e.g. m=0:4, to compute multiple characteristic values efficiently.

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