DLMF:28.22.E14 (Q8381): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aldec
Property / Symbols used
 
Property / Symbols used: cotangent function / rank
 
Normal rank
Property / Symbols used: cotangent function / qualifier
 
Defining formula:

cot z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}

\cot@@{\NVar{z}}
Property / Symbols used: cotangent function / qualifier
 
xml-id: C4.S14.E7.m2adec
Property / Symbols used
 
Property / Symbols used: Q12301 / rank
 
Normal rank
Property / Symbols used: Q12301 / qualifier
 
Defining formula:

M ν ( j ) ( z , h ) modified-Mathieu-M 𝑗 𝜈 𝑧 {\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}

\modMathieuM{\NVar{j}}{\NVar{\nu}}@{\NVar{z}}{\NVar{h}}
Property / Symbols used: Q12301 / qualifier
 
xml-id: C28.S20.SS3.p1.m4aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q12294 / rank
 
Normal rank
Property / Symbols used: Q12294 / qualifier
 
Defining formula:

h {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12294 / qualifier
 
xml-id: C28.S1.XMD11.m1mdec
Property / Symbols used
 
Property / Symbols used: Q12272 / rank
 
Normal rank
Property / Symbols used: Q12272 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q12272 / qualifier
 
xml-id: C28.S1.XMD6.m1edec
Property / Symbols used
 
Property / Symbols used: Q12278 / rank
 
Normal rank
Property / Symbols used: Q12278 / qualifier
 
Defining formula:

ν 𝜈 {\displaystyle{\displaystyle\nu}}

\nu
Property / Symbols used: Q12278 / qualifier
 
xml-id: C28.S1.XMD7.m1adec

Latest revision as of 15:06, 2 January 2020

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DLMF:28.22.E14
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    Statements

    M ν ( 2 ) ( z , h ) = cot ( ν π ) M ν ( 1 ) ( z , h ) - 1 sin ( ν π ) M - ν ( 1 ) ( z , h ) . modified-Mathieu-M 2 𝜈 𝑧 𝜈 𝜋 modified-Mathieu-M 1 𝜈 𝑧 1 𝜈 𝜋 modified-Mathieu-M 1 𝜈 𝑧 {\displaystyle{\displaystyle{\mathrm{M}^{(2)}_{\nu}}\left(z,h\right)=\cot\left% (\nu\pi\right){\mathrm{M}^{(1)}_{\nu}}\left(z,h\right)-\frac{1}{\sin\left(\nu% \pi\right)}{\mathrm{M}^{(1)}_{-\nu}}\left(z,h\right).}}
    0 references
    DLMF:28.22.E14
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aldec
    0 references
    cot z 𝑧 {\displaystyle{\displaystyle\cot\NVar{z}}}
    C4.S14.E7.m2adec
    0 references
    M ν ( j ) ( z , h ) modified-Mathieu-M 𝑗 𝜈 𝑧 {\displaystyle{\displaystyle{\mathrm{M}^{(\NVar{j})}_{\NVar{\nu}}}\left(\NVar{% z},\NVar{h}\right)}}
    C28.S20.SS3.p1.m4aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references
    h {\displaystyle{\displaystyle h}}
    C28.S1.XMD11.m1mdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C28.S1.XMD6.m1edec
    0 references
    ν 𝜈 {\displaystyle{\displaystyle\nu}}
    C28.S1.XMD7.m1adec
    0 references