Formula:9021

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Digital Library of Mathematical Functions ID 28.16.E1

λ ν ( h 2 ) - 2 h 2 + 2 s h - 1 8 ( s 2 + 1 ) - 1 2 7 h ( s 3 + 3 s ) - 1 2 12 h 2 ( 5 s 4 + 34 s 2 + 9 ) - 1 2 17 h 3 ( 33 s 5 + 410 s 3 + 405 s ) - 1 2 20 h 4 ( 63 s 6 + 1260 s 4 + 2943 s 2 + 486 ) - 1 2 25 h 5 ( 527 s 7 + 15617 s 5 + 69001 s 3 + 41607 s ) + . asymptotic-expansion Mathieu-eigenvalue-lambda 𝜈 superscript 2 2 superscript 2 2 𝑠 1 8 superscript 𝑠 2 1 1 superscript 2 7 superscript 𝑠 3 3 𝑠 1 superscript 2 12 superscript 2 5 superscript 𝑠 4 34 superscript 𝑠 2 9 1 superscript 2 17 superscript 3 33 superscript 𝑠 5 410 superscript 𝑠 3 405 𝑠 1 superscript 2 20 superscript 4 63 superscript 𝑠 6 1260 superscript 𝑠 4 2943 superscript 𝑠 2 486 1 superscript 2 25 superscript 5 527 superscript 𝑠 7 15617 superscript 𝑠 5 69001 superscript 𝑠 3 41607 𝑠 {\displaystyle{\displaystyle\lambda_{\nu}\left(h^{2}\right)\sim-2h^{2}+2sh-% \dfrac{1}{8}(s^{2}+1)-\dfrac{1}{2^{7}h}(s^{3}+3s)-\dfrac{1}{2^{12}h^{2}}(5s^{4% }+34s^{2}+9)-\dfrac{1}{2^{17}h^{3}}(33s^{5}+410s^{3}+405s)-\dfrac{1}{2^{20}h^{% 4}}(63s^{6}+1260s^{4}+2943s^{2}+486)-\dfrac{1}{2^{25}h^{5}}(527s^{7}+15617s^{5% }+69001s^{3}+41607s)+\cdots.}}


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