DLMF:6.5.E3 (Q2243): Difference between revisions

From DRMF
Jump to navigation Jump to search
Created a new Item: Wikidata Toolkit example test item creation
 
Changed an Item: Add constraint
 
(5 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: exponential integral / rank
 
Normal rank
Property / Symbols used: exponential integral / qualifier
 
Defining formula:

E 1 ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}

\expintE@{\NVar{z}}
Property / Symbols used: exponential integral / qualifier
 
xml-id: C6.S2.E1.m2abdec
Property / Symbols used
 
Property / Symbols used: Q11306 / rank
 
Normal rank
Property / Symbols used: Q11306 / qualifier
 
Defining formula:

Ei ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}

\expintEi@{\NVar{x}}
Property / Symbols used: Q11306 / qualifier
 
xml-id: C6.S2.SS1.p3.m2abdec
Property / Symbols used
 
Property / Symbols used: hyperbolic sine integral / rank
 
Normal rank
Property / Symbols used: hyperbolic sine integral / qualifier
 
Defining formula:

Shi ( z ) hyperbolic-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Shi}\left(\NVar{z}\right)}}

\sinhint@{\NVar{z}}
Property / Symbols used: hyperbolic sine integral / qualifier
 
xml-id: C6.S2.E15.m2adec
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.m2abdec
Property / Symbols used
 
Property / Symbols used: sine integral / rank
 
Normal rank
Property / Symbols used: sine integral / qualifier
 
Defining formula:

Si ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}

\sinint@{\NVar{z}}
Property / Symbols used: sine integral / qualifier
 
xml-id: C6.S2.E9.m2adec
Property / Symbols used
 
Property / Symbols used: Q11307 / rank
 
Normal rank
Property / Symbols used: Q11307 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11307 / qualifier
 
xml-id: C6.S1.XMD1.m1bdec

Latest revision as of 01:24, 2 January 2020

No description defined
Language Label Description Also known as
English
DLMF:6.5.E3
No description defined

    Statements

    1 2 ( Ei ( x ) + E 1 ( x ) ) = Shi ( x ) = - i Si ( i x ) , 1 2 exponential-integral-Ei 𝑥 exponential-integral 𝑥 hyperbolic-sine-integral 𝑥 𝑖 sine-integral 𝑖 𝑥 {\displaystyle{\displaystyle\tfrac{1}{2}(\mathrm{Ei}\left(x\right)+E_{1}\left(% x\right))=\mathrm{Shi}\left(x\right)=-i\mathrm{Si}\left(ix\right),}}
    0 references
    DLMF:6.5.E3
    0 references
    E 1 ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    C6.S2.E1.m2abdec
    0 references
    Ei ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    C6.S2.SS1.p3.m2abdec
    0 references
    Shi ( z ) hyperbolic-sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Shi}\left(\NVar{z}\right)}}
    C6.S2.E15.m2adec
    0 references
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    C1.S9.E1.m2abdec
    0 references
    Si ( z ) sine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Si}\left(\NVar{z}\right)}}
    C6.S2.E9.m2adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C6.S1.XMD1.m1bdec
    0 references