DLMF:2.11.E21 (Q1046): 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
 
Defining formula:

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

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2andec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
Defining formula:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2aidec
Property / Symbols used
 
Property / Symbols used: terminant function / rank
 
Normal rank
Property / Symbols used: terminant function / qualifier
 
Defining formula:

F p ⁡ ( z ) terminant-function 𝑝 𝑧 {\displaystyle{\displaystyle F_{\NVar{p}}\left(\NVar{z}\right)}}

\terminant{\NVar{p}}@{\NVar{z}}
Property / Symbols used: terminant function / qualifier
 
xml-id: C2.S11.E11.m2afdec
Property / Symbols used
 
Property / Symbols used: Q11141 / rank
 
Normal rank
Property / Symbols used: Q11141 / qualifier
 
Defining formula:

R n ( j ) ⁢ ( z ) superscript subscript 𝑅 𝑛 𝑗 𝑧 {\displaystyle{\displaystyle R_{n}^{(j)}(z)}}

R_{n}^{(j)}(z)
Property / Symbols used: Q11141 / qualifier
 
xml-id: C2.S11.XMD10.m1bdec
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.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11055 / rank
 
Normal rank
Property / Symbols used: Q11055 / qualifier
 
Defining formula:

λ j subscript 𝜆 𝑗 {\displaystyle{\displaystyle\lambda_{j}}}

\lambda_{j}
Property / Symbols used: Q11055 / qualifier
 
xml-id: C2.S7.XMD14.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11056 / rank
 
Normal rank
Property / Symbols used: Q11056 / qualifier
 
Defining formula:

μ j subscript 𝜇 𝑗 {\displaystyle{\displaystyle\mu_{j}}}

\mu_{j}
Property / Symbols used: Q11056 / qualifier
 
xml-id: C2.S7.XMD15.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11143 / rank
 
Normal rank
Property / Symbols used: Q11143 / qualifier
 
Defining formula:

C 1 subscript 𝐶 1 {\displaystyle{\displaystyle C_{1}}}

C_{1}
Property / Symbols used: Q11143 / qualifier
 
xml-id: C2.S7.XMD18.m1adec

Latest revision as of 17:42, 1 January 2020

No description defined
Language Label Description Also known as
English
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
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2aidec
    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.m2afdec
    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.m1bdec
    0 references
    Q11142
    Defining formula
    a s , j subscript 𝑎 𝑠 𝑗 {\displaystyle{\displaystyle a_{s,j}}}
    xml-id
    C2.S11.XMD9.m1bdec
    0 references
    Q11055
    Defining formula
    λ j subscript 𝜆 𝑗 {\displaystyle{\displaystyle\lambda_{j}}}
    xml-id
    C2.S7.XMD14.m1bdec
    0 references
    Q11056
    Defining formula
    μ j subscript 𝜇 𝑗 {\displaystyle{\displaystyle\mu_{j}}}
    xml-id
    C2.S7.XMD15.m1bdec
    0 references
    Q11143
    Defining formula
    C 1 subscript 𝐶 1 {\displaystyle{\displaystyle C_{1}}}
    xml-id
    C2.S7.XMD18.m1adec
    0 references
     
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