DLMF:28.8.E1 (Q8265)

From DRMF
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:28.8.E1
No description defined

    Statements

    Defining formula
    a m ⁡ ( h 2 ) b m + 1 ⁡ ( 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 selection Mathieu-eigenvalue-a 𝑚 superscript ℎ 2 Mathieu-eigenvalue-b 𝑚 1 superscript ℎ 2 2 superscript ℎ 2 2 𝑠 ℎ 1 8 superscript 𝑠 2 1 1 superscript 2 7 ℎ superscript 𝑠 3 3 𝑠 1 superscript 2 12 superscript ℎ 2 5 superscript 𝑠 4 34 superscript 𝑠 2 9 1 superscript 2 17 superscript ℎ 3 33 superscript 𝑠 5 410 superscript 𝑠 3 405 𝑠 1 superscript 2 20 superscript ℎ 4 63 superscript 𝑠 6 1260 superscript 𝑠 4 2943 superscript 𝑠 2 486 1 superscript 2 25 superscript ℎ 5 527 superscript 𝑠 7 15617 superscript 𝑠 5 69001 superscript 𝑠 3 41607 𝑠 ⋯ {\displaystyle{\displaystyle\rselection{a_{m}\left(h^{2}\right)\\ b_{m+1}\left(h^{2}\right)}\sim-2h^{2}+2sh-\frac{1}{8}(s^{2}+1)-\frac{1}{2^{7}h% }(s^{3}+3s)-\frac{1}{2^{12}h^{2}}(5s^{4}+34s^{2}+9)-\frac{1}{2^{17}h^{3}}(33s^% {5}+410s^{3}+405s)-\frac{1}{2^{20}h^{4}}(63s^{6}+1260s^{4}+2943s^{2}+486)-% \frac{1}{2^{25}h^{5}}(527s^{7}+15617s^{5}+69001s^{3}+41607s)+\cdots.}}
    0 references
    DLMF id
    DLMF:28.8.E1
    0 references
    Symbols used
    Q12281
    Defining formula
    a n ⁡ ( q ) Mathieu-eigenvalue-a 𝑛 𝑞 {\displaystyle{\displaystyle a_{\NVar{n}}\left(\NVar{q}\right)}}
    xml-id
    C28.S2.SS5.p1.m3adec
    0 references
    Q12282
    Defining formula
    b n ⁡ ( q ) Mathieu-eigenvalue-b 𝑛 𝑞 {\displaystyle{\displaystyle b_{\NVar{n}}\left(\NVar{q}\right)}}
    xml-id
    C28.S2.SS5.p1.m4adec
    0 references
    Q10931
    Defining formula
    ∼ asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.SS3.p1.m11adec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1dec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8265&oldid=50869"