DLMF:19.32.E2 (Q6692): Difference between revisions

From DRMF
Jump to navigation Jump to search
← Older edit
‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
 
(2 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10901 / rank
 
Normal rank
Property / Symbols used: Q10901 / qualifier
 
Defining formula:

ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}

\imagpart@@
Property / Symbols used: Q10901 / qualifier
 
xml-id: C1.S9.E2.m2adec
Property / Symbols used
 
Property / Symbols used: Q10817 / rank
 
Normal rank
Property / Symbols used: Q10817 / qualifier
 
Defining formula:

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

\phase
Property / Symbols used: Q10817 / qualifier
 
xml-id: C1.S9.E7.m1adec
Property / Symbols used
 
Property / Symbols used: Q11923 / rank
 
Normal rank
Property / Symbols used: Q11923 / qualifier
 
Defining formula:

z ⁢ ( p ) 𝑧 𝑝 {\displaystyle{\displaystyle z(p)}}

z(p)
Property / Symbols used: Q11923 / qualifier
 
xml-id: C19.S32.XMD1.m1adec

Latest revision as of 14:24, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:19.32.E2
No description defined

    Statements

    Defining formula
    d z = - 1 2 ⁢ ( ∏ j = 1 3 ( p - x j ) - 1 / 2 ) ⁢ d p , 𝑧 1 2 superscript subscript product 𝑗 1 3 superscript 𝑝 subscript 𝑥 𝑗 1 2 𝑝 {\displaystyle{\displaystyle\mathrm{d}z=-\frac{1}{2}\left(\prod_{j=1}^{3}(p-x_% {j})^{-1/2}\right)\mathrm{d}p,}}
    0 references
    DLMF id
    DLMF:19.32.E2
    0 references
    constraint
    ℑ ⁡ p > 0 𝑝 0 {\displaystyle{\displaystyle\Im p>0}}
    0 references
    0 < ph ⁡ ( p - x j ) < π 0 phase 𝑝 subscript 𝑥 𝑗 𝜋 {\displaystyle{\displaystyle 0<\operatorname{ph}\left(p-x_{j}\right)<\pi}}
    0 references
    ℑ ⁡ p > 0 𝑝 0 {\displaystyle{\displaystyle\Im p>0}}
    0 references
    0 < ph ⁡ ( p - x j ) < π 0 ph 𝑝 subscript 𝑥 𝑗 𝜋 {\displaystyle{\displaystyle 0<\operatorname{ph}\left(p-x_{j}\right)<\pi}}
    0 references
    j = 1 , 2 , 3 𝑗 1 2 3 {\displaystyle{\displaystyle j=1,2,3}}
    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.m2adec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1adec
    0 references
    Q10901
    Defining formula
    ℑ ⁡ absent {\displaystyle{\displaystyle\Im}}
    xml-id
    C1.S9.E2.m2adec
    0 references
    Q10817
    Defining formula
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    Q11923
    Defining formula
    z ⁢ ( p ) 𝑧 𝑝 {\displaystyle{\displaystyle z(p)}}
    xml-id
    C19.S32.XMD1.m1adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q6692&oldid=46771"