DLMF:2.11.E17 (Q1042): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
test:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2ajdec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2afdec
Property / Symbols used
 
Property / Symbols used: Q11137 / rank
 
Normal rank
Property / Symbols used: Q11137 / qualifier
 
test:

θ 𝜃 {\displaystyle{\displaystyle\theta}}

\theta
Property / Symbols used: Q11137 / qualifier
 
xml-id: C2.S11.XMD4.m1edec
Property / Symbols used
 
Property / Symbols used: Q11138 / rank
 
Normal rank
Property / Symbols used: Q11138 / qualifier
 
test:

a 2 ⁢ s ⁢ ( θ , α ) subscript 𝑎 2 𝑠 𝜃 𝛼 {\displaystyle{\displaystyle a_{2s}(\theta,\alpha)}}

a_{2s}(\theta,\alpha)
Property / Symbols used: Q11138 / qualifier
 
xml-id: C2.S11.XMD6.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11139 / rank
 
Normal rank
Property / Symbols used: Q11139 / qualifier
 
test:

c ⁢ ( θ ) 𝑐 𝜃 {\displaystyle{\displaystyle c(\theta)}}

c(\theta)
Property / Symbols used: Q11139 / qualifier
 
xml-id: C2.S11.XMD7.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11140 / rank
 
Normal rank
Property / Symbols used: Q11140 / qualifier
 
test:

h 2 ⁢ s ⁢ ( θ , α ) subscript ℎ 2 𝑠 𝜃 𝛼 {\displaystyle{\displaystyle h_{2s}(\theta,\alpha)}}

h_{2s}(\theta,\alpha)
Property / Symbols used: Q11140 / qualifier
 
xml-id: C2.S11.XMD8.m1adec

Latest revision as of 16:41, 1 January 2020

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English
DLMF:2.11.E17
No description defined

    Statements

    test
    h 2 ⁢ s ⁢ ( θ , α ) = e i ⁢ α ⁢ ( π - θ ) 1 + e - i ⁢ θ ⁢ a 2 ⁢ s ⁢ ( θ , α ) + ( - 1 ) s - 1 ⁢ i ⁢ 1 ⋅ 3 ⋅ 5 ⁢ ⋯ ⁢ ( 2 ⁢ s - 1 ) ( c ⁢ ( θ ) ) 2 ⁢ s + 1 , subscript ℎ 2 𝑠 𝜃 𝛼 superscript 𝑒 𝑖 𝛼 𝜋 𝜃 1 superscript 𝑒 𝑖 𝜃 subscript 𝑎 2 𝑠 𝜃 𝛼 superscript 1 𝑠 1 𝑖 ⋅ 1 3 5 ⋯ 2 𝑠 1 superscript 𝑐 𝜃 2 𝑠 1 {\displaystyle{\displaystyle h_{2s}(\theta,\alpha)=\frac{e^{i\alpha(\pi-\theta% )}}{1+e^{-i\theta}}a_{2s}(\theta,\alpha)+(-1)^{s-1}i\frac{1\cdot 3\cdot 5\cdot% \cdot\cdot(2s-1)}{(c(\theta))^{2s+1}},}}
    0 references
    DLMF id
    DLMF:2.11.E17
    0 references
    comment
    Warning: Falling back to standard tex;
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aidec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2ajdec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2afdec
    0 references
    Q11137
    test
    θ 𝜃 {\displaystyle{\displaystyle\theta}}
    xml-id
    C2.S11.XMD4.m1edec
    0 references
    Q11138
    test
    a 2 ⁢ s ⁢ ( θ , α ) subscript 𝑎 2 𝑠 𝜃 𝛼 {\displaystyle{\displaystyle a_{2s}(\theta,\alpha)}}
    xml-id
    C2.S11.XMD6.m1bdec
    0 references
    Q11139
    test
    c ⁢ ( θ ) 𝑐 𝜃 {\displaystyle{\displaystyle c(\theta)}}
    xml-id
    C2.S11.XMD7.m1bdec
    0 references
    Q11140
    test
    h 2 ⁢ s ⁢ ( θ , α ) subscript ℎ 2 𝑠 𝜃 𝛼 {\displaystyle{\displaystyle h_{2s}(\theta,\alpha)}}
    xml-id
    C2.S11.XMD8.m1adec
    0 references
     
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