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DLMF:28.2.E39

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Formula:8878
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MaRDI QIDQ8878

  • Label: DLMF:28.2.E39


Digital Library of Mathematical Functions ID 28.2.E39

se n ⁡ ( z , q ) se n ′ ⁡ ( 0 , q ) = w II ⁢ ( z ; b n ⁡ ( q ) , q ) , Mathieu-se 𝑛 𝑧 𝑞 diffop Mathieu-se 𝑛 1 0 𝑞 subscript 𝑤 II 𝑧 Mathieu-eigenvalue-b 𝑛 𝑞 𝑞 {\displaystyle{\displaystyle\frac{\mathrm{se}_{n}\left(z,q\right)}{\mathrm{se}% _{n}'\left(0,q\right)}=w_{\mbox{\tiny II}}(z;b_{n}\left(q\right),q),}}


Constraint(s)

n = 1 , 2 , … 𝑛 1 2 … {\displaystyle{\displaystyle n=1,2,\dots}}

Symbols List

  • b n ⁡ ( q ) Mathieu-eigenvalue-b 𝑛 𝑞 {\displaystyle{\displaystyle b_{\NVar{n}}\left(\NVar{q}\right)}} :
  • se n ⁡ ( z , q ) Mathieu-se 𝑛 𝑧 𝑞 {\displaystyle{\displaystyle\mathrm{se}_{\NVar{n}}\left(\NVar{z},\NVar{q}% \right)}} :
  • q = h 2 𝑞 superscript ℎ 2 {\displaystyle{\displaystyle q=h^{2}}} : parameter
  • n 𝑛 {\displaystyle{\displaystyle n}} : integer
  • z 𝑧 {\displaystyle{\displaystyle z}} : complex variable
  • w II ⁢ ( z ; a , q ) subscript 𝑤 II 𝑧 𝑎 𝑞 {\displaystyle{\displaystyle w_{\mbox{\tiny II}}(z;a,q)}} : fundamental solution
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This page was last edited on 28 January 2024, at 10:30.
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