DLMF:2.11.E20 (Q1045): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: Q11142 / rank
 
Normal rank
Property / Symbols used: Q11142 / qualifier
 
Defining formula:

a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}

a_{s,j}
Property / Symbols used: Q11142 / qualifier
 
xml-id: C2.S11.XMD9.m1adec

Revision as of 17:41, 1 January 2020

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DLMF:2.11.E20
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    Statements

    Defining formula
    R n ( 1 ) ⁢ ( z ) = ( - 1 ) n - 1 ⁢ i ⁢ e ( μ 2 - μ 1 ) ⁢ π ⁢ i ⁢ e λ 2 ⁢ z ⁢ z μ 2 ⁢ ( C 1 ⁢ ∑ s = 0 m - 1 ( - 1 ) s ⁢ a s , 2 ⁢ F n + μ 2 - μ 1 - s ⁡ ( z ) z s + R m , n ( 1 ) ⁢ ( z ) ) , superscript subscript 𝑅 𝑛 1 𝑧 superscript 1 𝑛 1 𝑖 superscript 𝑒 subscript 𝜇 2 subscript 𝜇 1 𝜋 𝑖 superscript 𝑒 subscript 𝜆 2 𝑧 superscript 𝑧 subscript 𝜇 2 subscript 𝐶 1 superscript subscript 𝑠 0 𝑚 1 superscript 1 𝑠 subscript 𝑎 𝑠 2 terminant-function 𝑛 subscript 𝜇 2 subscript 𝜇 1 𝑠 𝑧 superscript 𝑧 𝑠 superscript subscript 𝑅 𝑚 𝑛 1 𝑧 {\displaystyle{\displaystyle R_{n}^{(1)}(z)=(-1)^{n-1}ie^{(\mu_{2}-\mu_{1})\pi i% }e^{\lambda_{2}z}z^{\mu_{2}}\left(C_{1}\sum_{s=0}^{m-1}(-1)^{s}a_{s,2}\frac{F_% {n+\mu_{2}-\mu_{1}-s}\left(z\right)}{z^{s}}+R_{m,n}^{(1)}(z)\right),}}
    0 references
    DLMF id
    DLMF:2.11.E20
    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.m2akdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2amdec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2ahdec
    0 references
    terminant function
    Defining formula
    F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}
    xml-id
    C2.S11.E11.m2aedec
    0 references
    Q11141
    Defining formula
    R n ( j ) ⁢ ( z ) superscript subscript 𝑅 𝑛 𝑗 𝑧 {\displaystyle{\displaystyle R_{n}^{(j)}(z)}}
    xml-id
    C2.S11.XMD10.m1adec
    0 references
    Q11142
    Defining formula
    a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}
    xml-id
    C2.S11.XMD9.m1adec
    0 references
     
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