DLMF:1.9.E21 (Q265): Difference between revisions

From MaRDI portal
Changed an Item: Remove DLMF prefix from DLMF id
Added link to MaRDI item.
 
(8 intermediate revisions by 3 users not shown)
Property / constraint
 

n = 1 , 2 , 𝑛 1 2 {\displaystyle{\displaystyle n=1,2,\dots}}

n=1,2,\dots
Property / constraint: n = 1 , 2 , 𝑛 1 2 {\displaystyle{\displaystyle n=1,2,\dots}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: Q10728 / rank
 
Normal rank
Property / Symbols used: Q10728 / qualifier
 
DLMF defining formula:

( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}

\binom{\NVar{m}}{\NVar{n}}
Property / Symbols used: Q10728 / qualifier
 
xml-id: C1.S2.SS1.m1adec
Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
DLMF defining formula:

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

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2agdec
Property / Symbols used
 
Property / Symbols used: variable / rank
 
Normal rank
Property / Symbols used: variable / qualifier
 
DLMF defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: variable / qualifier
 
xml-id: C1.S1.XMD1.m1odec
Property / Symbols used
 
Property / Symbols used: nonnegative integer / rank
 
Normal rank
Property / Symbols used: nonnegative integer / qualifier
 
DLMF defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: nonnegative integer / qualifier
 
xml-id: C1.S1.XMD7.m1adec
Property / instance of
 
Property / instance of: Digital Library of Mathematical Functions Formula / rank
 
Normal rank
Property / MaRDI profile type
 
Property / MaRDI profile type: MaRDI formula profile / rank
 
Normal rank
links / mardi / namelinks / mardi / name
 

Latest revision as of 00:49, 3 March 2024

No description defined
Language Label Description Also known as
English
DLMF:1.9.E21
No description defined

    Statements

    z n = ( x n - ( n 2 ) x n - 2 y 2 + ( n 4 ) x n - 4 y 4 - ) + i ( ( n 1 ) x n - 1 y - ( n 3 ) x n - 3 y 3 + ) , superscript 𝑧 𝑛 superscript 𝑥 𝑛 binomial 𝑛 2 superscript 𝑥 𝑛 2 superscript 𝑦 2 binomial 𝑛 4 superscript 𝑥 𝑛 4 superscript 𝑦 4 𝑖 binomial 𝑛 1 superscript 𝑥 𝑛 1 𝑦 binomial 𝑛 3 superscript 𝑥 𝑛 3 superscript 𝑦 3 {\displaystyle{\displaystyle z^{n}=\left(x^{n}-\genfrac{(}{)}{0.0pt}{}{n}{2}x^% {n-2}y^{2}+\genfrac{(}{)}{0.0pt}{}{n}{4}x^{n-4}y^{4}-\cdots\right)+i\left(% \genfrac{(}{)}{0.0pt}{}{n}{1}x^{n-1}y-\genfrac{(}{)}{0.0pt}{}{n}{3}x^{n-3}y^{3% }+\cdots\right),}}
    0 references
    n = 1 , 2 , 𝑛 1 2 {\displaystyle{\displaystyle n=1,2,\dots}}
    0 references
    ( m n ) binomial 𝑚 𝑛 {\displaystyle{\displaystyle\genfrac{(}{)}{0.0pt}{}{\NVar{m}}{\NVar{n}}}}
    C1.S2.SS1.m1adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2agdec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C1.S1.XMD1.m1odec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C1.S1.XMD7.m1adec
    0 references

    Identifiers