DLMF:30.9.E1 (Q8878): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
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Property / Symbols used
 
Property / Symbols used: Q12407 / rank
 
Normal rank
Property / Symbols used: Q12407 / qualifier
 
Defining formula:

λ n m ( γ 2 ) spheroidal-eigenvalue-lambda 𝑚 𝑛 superscript 𝛾 2 {\displaystyle{\displaystyle\lambda^{\NVar{m}}_{\NVar{n}}\left(\NVar{\gamma^{2% }}\right)}}

\spheigvalLambda{\NVar{m}}{\NVar{n}}@{\NVar{\gamma^{2}}}
Property / Symbols used: Q12407 / qualifier
 
xml-id: C30.S3.SS1.p1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12408 / rank
 
Normal rank
Property / Symbols used: Q12408 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12408 / qualifier
 
xml-id: C30.S1.XMD4.m1dec
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.m1dec
Property / Symbols used
 
Property / Symbols used: Q12404 / rank
 
Normal rank
Property / Symbols used: Q12404 / qualifier
 
Defining formula:

γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}

\gamma^{2}
Property / Symbols used: Q12404 / qualifier
 
xml-id: C30.S2.XMD3.m1dec
Property / Symbols used
 
Property / Symbols used: Q12429 / rank
 
Normal rank
Property / Symbols used: Q12429 / qualifier
 
Defining formula:

q 𝑞 {\displaystyle{\displaystyle q}}

q
Property / Symbols used: Q12429 / qualifier
 
xml-id: C30.S9.XMD1.m1dec
Property / Symbols used
 
Property / Symbols used: Q12430 / rank
 
Normal rank
Property / Symbols used: Q12430 / qualifier
 
Defining formula:

β n subscript 𝛽 𝑛 {\displaystyle{\displaystyle\beta_{n}}}

\beta_{n}
Property / Symbols used: Q12430 / qualifier
 
xml-id: C30.S9.XMD2.m1dec

Latest revision as of 01:47, 2 January 2020

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DLMF:30.9.E1
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    Statements

    λ n m ( γ 2 ) - γ 2 + γ q + β 0 + β 1 γ - 1 + β 2 γ - 2 + , asymptotic-expansion spheroidal-eigenvalue-lambda 𝑚 𝑛 superscript 𝛾 2 superscript 𝛾 2 𝛾 𝑞 subscript 𝛽 0 subscript 𝛽 1 superscript 𝛾 1 subscript 𝛽 2 superscript 𝛾 2 {\displaystyle{\displaystyle\lambda^{m}_{n}\left(\gamma^{2}\right)\sim-\gamma^% {2}+\gamma q+\beta_{0}+\beta_{1}\gamma^{-1}+\beta_{2}\gamma^{-2}+\cdots,}}
    0 references
    DLMF:30.9.E1
    0 references
    asymptotic-expansion {\displaystyle{\displaystyle\sim}}
    C2.S1.SS3.p1.m11adec
    0 references
    λ n m ( γ 2 ) spheroidal-eigenvalue-lambda 𝑚 𝑛 superscript 𝛾 2 {\displaystyle{\displaystyle\lambda^{\NVar{m}}_{\NVar{n}}\left(\NVar{\gamma^{2% }}\right)}}
    C30.S3.SS1.p1.m2adec
    0 references
    m 𝑚 {\displaystyle{\displaystyle m}}
    C30.S1.XMD4.m1dec
    0 references
    n m 𝑛 𝑚 {\displaystyle{\displaystyle n\geq m}}
    C30.S1.XMD5.m1dec
    0 references
    γ 2 superscript 𝛾 2 {\displaystyle{\displaystyle\gamma^{2}}}
    C30.S2.XMD3.m1dec
    0 references
    q 𝑞 {\displaystyle{\displaystyle q}}
    C30.S9.XMD1.m1dec
    0 references
    β n subscript 𝛽 𝑛 {\displaystyle{\displaystyle\beta_{n}}}
    C30.S9.XMD2.m1dec
    0 references