DLMF:28.26.E2 (Q8418): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q12284 / rank
 
Normal rank
Property / Symbols used: Q12284 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q12284 / qualifier
 
xml-id: C28.S1.XMD1.m1adec
Property / Symbols used
 
Property / Symbols used: Q12294 / rank
 
Normal rank
Property / Symbols used: Q12294 / qualifier
 
Defining formula:

h ℎ {\displaystyle{\displaystyle h}}

h
Property / Symbols used: Q12294 / qualifier
 
xml-id: C28.S1.XMD11.m1adec
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.m1adec
Property / Symbols used
 
Property / Symbols used: Q12310 / rank
 
Normal rank
Property / Symbols used: Q12310 / qualifier
 
Defining formula:

ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}

\phi
Property / Symbols used: Q12310 / qualifier
 
xml-id: C28.S26.XMD1.m1adec

Latest revision as of 15:15, 2 January 2020

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English
DLMF:28.26.E2
No description defined

    Statements

    Defining formula
    i ⁢ Ms m + 1 ( 3 ) ⁡ ( z , h ) = e i ⁢ ϕ ( π ⁢ h ⁢ cosh ⁡ z ) 1 / 2 ⁢ ( \MathieuFs ⁢ m ⁢ @ ⁢ z ⁢ h - i ⁢ \MathieuGs ⁢ m ⁢ @ ⁢ z ⁢ h ) , imaginary-unit modified-Mathieu-Ms 3 𝑚 1 𝑧 ℎ superscript 𝑒 imaginary-unit italic-ϕ superscript 𝜋 ℎ 𝑧 1 2 \MathieuFs 𝑚 @ 𝑧 ℎ imaginary-unit \MathieuGs 𝑚 @ 𝑧 ℎ {\displaystyle{\displaystyle\mathrm{i}{\mathrm{Ms}^{(3)}_{m+1}}\left(z,h\right% )=\dfrac{e^{\mathrm{i}\phi}}{(\pi h\cosh z)^{\ifrac{1}{2}}}\*{\left(\MathieuFs% {m}@{z}{h}-\mathrm{i}\MathieuGs{m}@{z}{h}\right)},}}
    0 references
    DLMF id
    DLMF:28.26.E2
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aadec
    0 references
    hyperbolic cosine function
    Defining formula
    cosh ⁡ z 𝑧 {\displaystyle{\displaystyle\cosh\NVar{z}}}
    xml-id
    C4.S28.E2.m2aadec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aadec
    0 references
    radial Mathieu function
    Defining formula
    Ms n ( j ) ⁡ ( z , h ) modified-Mathieu-Ms 𝑗 𝑛 𝑧 ℎ {\displaystyle{\displaystyle{\mathrm{Ms}^{(\NVar{j})}_{\NVar{n}}}\left(\NVar{z% },\NVar{h}\right)}}
    xml-id
    C28.S20.E16.m2adec
    0 references
    Q12284
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C28.S1.XMD1.m1adec
    0 references
    Q12294
    Defining formula
    h ℎ {\displaystyle{\displaystyle h}}
    xml-id
    C28.S1.XMD11.m1adec
    0 references
    Q12272
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C28.S1.XMD6.m1adec
    0 references
    Q12310
    Defining formula
    ϕ italic-ϕ {\displaystyle{\displaystyle\phi}}
    xml-id
    C28.S26.XMD1.m1adec
    0 references
     
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