DLMF:30.5.E4 (Q8857): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older editNewer edit →
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q12409 / rank
 
Normal rank
Property / Symbols used: Q12409 / qualifier
 
Defining formula:

n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}

n\geq m
Property / Symbols used: Q12409 / qualifier
 
xml-id: C30.S1.XMD5.m1cdec

Revision as of 01:44, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:30.5.E4
No description defined

    Statements

    Defining formula
    𝒲 ⁡ { 𝖯𝗌 n m ⁡ ( x , γ 2 ) , 𝖰𝗌 n m ⁡ ( x , γ 2 ) } = ( n + m ) ! ( 1 - x 2 ) ⁢ ( n - m ) ! ⁢ A n m ⁢ ( γ 2 ) ⁢ A n - m ⁢ ( γ 2 ) ( ≠ 0 ) , Wronskian spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 spheroidal-wave-on-cut-Qs 𝑚 𝑛 𝑥 superscript 𝛾 2 annotated 𝑛 𝑚 1 superscript 𝑥 2 𝑛 𝑚 superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 superscript subscript 𝐴 𝑛 𝑚 superscript 𝛾 2 absent 0 {\displaystyle{\displaystyle\mathscr{W}\left\{\mathsf{Ps}^{m}_{n}\left(x,% \gamma^{2}\right),\mathsf{Qs}^{m}_{n}\left(x,\gamma^{2}\right)\right\}=\frac{(% n+m)!}{(1-x^{2})(n-m)!}A_{n}^{m}(\gamma^{2})A_{n}^{-m}(\gamma^{2})\quad(\neq 0% ),}}
    0 references
    DLMF id
    DLMF:30.5.E4
    0 references
    Symbols used
    Q10865
    Defining formula
    𝒲 Wronskian {\displaystyle{\displaystyle\mathscr{W}}}
    xml-id
    C1.S13.Px2.p1.m3adec
    0 references
    Q10755
    Defining formula
    ! {\displaystyle{\displaystyle!}}
    xml-id
    introduction.Sx4.p1.t1.r15.m5adec
    0 references
    Q12418
    Defining formula
    𝖯𝗌 n m ⁡ ( x , γ 2 ) spheroidal-wave-on-cut-Ps 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathsf{Ps}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S4.SS1.m1adec
    0 references
    Q12421
    Defining formula
    𝖰𝗌 n m ⁡ ( x , γ 2 ) spheroidal-wave-on-cut-Qs 𝑚 𝑛 𝑥 superscript 𝛾 2 {\displaystyle{\displaystyle\mathsf{Qs}^{\NVar{m}}_{\NVar{n}}\left(\NVar{x},% \NVar{\gamma^{2}}\right)}}
    xml-id
    C30.S5.m1acdec
    0 references
    Q12419
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C30.S1.XMD2.m1cdec
    0 references
    Q12408
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C30.S1.XMD4.m1cdec
    0 references
    Q12409
    Defining formula
    n ≥ m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    xml-id
    C30.S1.XMD5.m1cdec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q8857&oldid=34165"