DLMF:2.11.E21 (Q1046): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2andec

Revision as of 17:42, 1 January 2020

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DLMF:2.11.E21
No description defined

    Statements

    Defining formula
    R n ( 2 ) ⁢ ( z ) = ( - 1 ) n ⁢ i ⁢ e ( μ 2 - μ 1 ) ⁢ π ⁢ i ⁢ e λ 1 ⁢ z ⁢ z μ 1 ⁢ ( C 2 ⁢ ∑ s = 0 m - 1 ( - 1 ) s ⁢ a s , 1 ⁢ F n + μ 1 - μ 2 - s ⁡ ( z ⁢ e - π ⁢ i ) z s + R m , n ( 2 ) ⁢ ( z ) ) , superscript subscript 𝑅 𝑛 2 𝑧 superscript 1 𝑛 𝑖 superscript 𝑒 subscript 𝜇 2 subscript 𝜇 1 𝜋 𝑖 superscript 𝑒 subscript 𝜆 1 𝑧 superscript 𝑧 subscript 𝜇 1 subscript 𝐶 2 superscript subscript 𝑠 0 𝑚 1 superscript 1 𝑠 subscript 𝑎 𝑠 1 terminant-function 𝑛 subscript 𝜇 1 subscript 𝜇 2 𝑠 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑧 𝑠 superscript subscript 𝑅 𝑚 𝑛 2 𝑧 {\displaystyle{\displaystyle R_{n}^{(2)}(z)=(-1)^{n}ie^{(\mu_{2}-\mu_{1})\pi i% }e^{\lambda_{1}z}z^{\mu_{1}}\left(C_{2}\sum_{s=0}^{m-1}(-1)^{s}a_{s,1}\frac{F_% {n+\mu_{1}-\mu_{2}-s}\left(ze^{-\pi i}\right)}{z^{s}}+R_{m,n}^{(2)}(z)\right),}}
    0 references
    DLMF id
    DLMF:2.11.E21
    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.m2aldec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2andec
    0 references
     
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