DLMF:8.11.E3 (Q2574): Difference between revisions

From testwiki
Jump to navigation Jump to search
imported>Admin
 
imported>Admin
 
(8 intermediate revisions by the same user not shown)
Property / constraint
 

| ph z | 3 2 π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}

|\phase@@{z}|\leq\tfrac{3}{2}\pi-\delta
Property / constraint: | ph z | 3 2 π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}} / rank
 
Normal rank
Property / Symbols used
 
Property / Symbols used: order not exceeding / rank
 
Normal rank
Property / Symbols used: order not exceeding / qualifier
 
test:

O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}

\bigO@{\NVar{x}}
Property / Symbols used: order not exceeding / qualifier
 
xml-id: C2.S1.E3.m2adec
Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
test:

ph phase {\displaystyle{\displaystyle\operatorname{ph}}}

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11323 / rank
 
Normal rank
Property / Symbols used: Q11323 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11323 / qualifier
 
xml-id: C8.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11324 / rank
 
Normal rank
Property / Symbols used: Q11324 / qualifier
 
test:

a 𝑎 {\displaystyle{\displaystyle a}}

a
Property / Symbols used: Q11324 / qualifier
 
xml-id: C8.S1.XMD3.m1bdec
Property / Symbols used
 
Property / Symbols used: Q11329 / rank
 
Normal rank
Property / Symbols used: Q11329 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11329 / qualifier
 
xml-id: C8.S1.XMD6.m1adec
Property / Symbols used
 
Property / Symbols used: Q11343 / rank
 
Normal rank
Property / Symbols used: Q11343 / qualifier
 
test:

δ 𝛿 {\displaystyle{\displaystyle\delta}}

\delta
Property / Symbols used: Q11343 / qualifier
 
xml-id: C8.S1.XMD7.m1dec
Property / Symbols used
 
Property / Symbols used: Q11342 / rank
 
Normal rank
Property / Symbols used: Q11342 / qualifier
 
test:

R n ( a , z ) subscript 𝑅 𝑛 𝑎 𝑧 {\displaystyle{\displaystyle R_{n}(a,z)}}

R_{n}(a,z)
Property / Symbols used: Q11342 / qualifier
 
xml-id: C8.S11.XMD2.m1adec

Latest revision as of 12:53, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:8.11.E3
No description defined

    Statements

    R n ( a , z ) = O ( z - n ) , subscript 𝑅 𝑛 𝑎 𝑧 Big-O superscript 𝑧 𝑛 {\displaystyle{\displaystyle R_{n}(a,z)=O\left(z^{-n}\right),}}
    0 references
    0 references
    | ph z | 3 2 π - δ phase 𝑧 3 2 𝜋 𝛿 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{3}{2}\pi-\delta}}
    0 references
    O ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    C2.S1.E3.m2adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2adec
    0 references
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    C1.S9.E7.m1adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C8.S1.XMD2.m1adec
    0 references
    a 𝑎 {\displaystyle{\displaystyle a}}
    C8.S1.XMD3.m1bdec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C8.S1.XMD6.m1adec
    0 references
    δ 𝛿 {\displaystyle{\displaystyle\delta}}
    C8.S1.XMD7.m1dec
    0 references
    R n ( a , z ) subscript 𝑅 𝑛 𝑎 𝑧 {\displaystyle{\displaystyle R_{n}(a,z)}}
    C8.S11.XMD2.m1adec
    0 references