DLMF:18.33.E1 (Q6007): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(7 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10770 / rank
 
Normal rank
Property / Symbols used: Q10770 / qualifier
 
Defining formula:

d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}

\diff{\NVar{x}}
Property / Symbols used: Q10770 / qualifier
 
xml-id: C1.S4.SS4.m1adec
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.m2adec
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

∫ {\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3adec
Property / Symbols used
 
Property / Symbols used: Q11729 / rank
 
Normal rank
Property / Symbols used: Q11729 / qualifier
 
Defining formula:

w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}

w(x)
Property / Symbols used: Q11729 / qualifier
 
xml-id: C18.S1.XMD10.m1dec
Property / Symbols used
 
Property / Symbols used: Q11750 / rank
 
Normal rank
Property / Symbols used: Q11750 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11750 / qualifier
 
xml-id: C18.S1.XMD2.m1dec
Property / Symbols used
 
Property / Symbols used: Q11730 / rank
 
Normal rank
Property / Symbols used: Q11730 / qualifier
 
Defining formula:

m 𝑚 {\displaystyle{\displaystyle m}}

m
Property / Symbols used: Q11730 / qualifier
 
xml-id: C18.S1.XMD5.m1dec
Property / Symbols used
 
Property / Symbols used: Q11726 / rank
 
Normal rank
Property / Symbols used: Q11726 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11726 / qualifier
 
xml-id: C18.S1.XMD6.m1dec
Property / Symbols used
 
Property / Symbols used: Q11791 / rank
 
Normal rank
Property / Symbols used: Q11791 / qualifier
 
Defining formula:

ϕ n ⁢ ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}

\phi_{n}(z)
Property / Symbols used: Q11791 / qualifier
 
xml-id: C18.S33.XMD1.m1dec

Latest revision as of 13:26, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:18.33.E1
No description defined

    Statements

    Defining formula
    1 2 ⁢ π ⁢ i ⁢ ∫ | z | = 1 ϕ n ⁢ ( z ) ⁢ ϕ m ⁢ ( z ) ¯ ⁢ w ⁢ ( z ) ⁢ d z z = δ n , m , 1 2 𝜋 imaginary-unit subscript 𝑧 1 subscript italic-ϕ 𝑛 𝑧 subscript italic-ϕ 𝑚 𝑧 𝑤 𝑧 𝑧 𝑧 Kronecker 𝑛 𝑚 {\displaystyle{\displaystyle\frac{1}{2\pi\mathrm{i}}\int_{|z|=1}\phi_{n}(z)% \overline{\phi_{m}(z)}w(z)\frac{\mathrm{d}z}{z}=\delta_{n,m},}}
    0 references
    DLMF id
    DLMF:18.33.E1
    0 references
    Symbols used
    Q10768
    Defining formula
    δ j , k Kronecker 𝑗 𝑘 {\displaystyle{\displaystyle\delta_{\NVar{j},\NVar{k}}}}
    xml-id
    introduction.Sx4.p1.t1.r4.m5adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2adec
    0 references
    complex conjugate
    Defining formula
    z ¯ 𝑧 {\displaystyle{\displaystyle\overline{\NVar{z}}}}
    xml-id
    C1.S9.E11.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
    Q10771
    Defining formula
    ∫ {\displaystyle{\displaystyle\int}}
    xml-id
    C1.S4.SS4.m3adec
    0 references
    Q11729
    Defining formula
    w ⁢ ( x ) 𝑤 𝑥 {\displaystyle{\displaystyle w(x)}}
    xml-id
    C18.S1.XMD10.m1dec
    0 references
    Q11750
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C18.S1.XMD2.m1dec
    0 references
    Q11730
    Defining formula
    m 𝑚 {\displaystyle{\displaystyle m}}
    xml-id
    C18.S1.XMD5.m1dec
    0 references
    Q11726
    Defining formula
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C18.S1.XMD6.m1dec
    0 references
    Q11791
    Defining formula
    ϕ n ⁢ ( z ) subscript italic-ϕ 𝑛 𝑧 {\displaystyle{\displaystyle\phi_{n}(z)}}
    xml-id
    C18.S33.XMD1.m1dec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6007&oldid=36554"