DLMF:6.5.E4 (Q2244): Difference between revisions

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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.m2acdec
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.m2acdec
Property / Symbols used
 
Property / Symbols used: hyperbolic cosine integral / rank
 
Normal rank
Property / Symbols used: hyperbolic cosine integral / qualifier
 
Defining formula:

Chi ⁡ ( z ) hyperbolic-cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Chi}\left(\NVar{z}\right)}}

\coshint@{\NVar{z}}
Property / Symbols used: hyperbolic cosine integral / qualifier
 
xml-id: C6.S2.E16.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.m2acdec
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.m1cdec

Latest revision as of 01:24, 2 January 2020

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DLMF:6.5.E4
No description defined

    Statements

    Defining formula
    1 2 ⁢ ( Ei ⁡ ( x ) - E 1 ⁡ ( x ) ) = Chi ⁡ ( x ) = Ci ⁡ ( i ⁢ x ) - 1 2 ⁢ π ⁢ i . 1 2 exponential-integral-Ei 𝑥 exponential-integral 𝑥 hyperbolic-cosine-integral 𝑥 cosine-integral 𝑖 𝑥 1 2 𝜋 𝑖 {\displaystyle{\displaystyle\tfrac{1}{2}(\mathrm{Ei}\left(x\right)-E_{1}\left(% x\right))=\mathrm{Chi}\left(x\right)=\mathrm{Ci}\left(ix\right)-\tfrac{1}{2}% \pi i.}}
    0 references
    DLMF id
    DLMF:6.5.E4
    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.m2aadec
    0 references
    cosine integral
    Defining formula
    Ci ⁡ ( z ) cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Ci}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E11.m2adec
    0 references
    exponential integral
    Defining formula
    E 1 ⁡ ( z ) exponential-integral 𝑧 {\displaystyle{\displaystyle E_{1}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E1.m2acdec
    0 references
    Q11306
    Defining formula
    Ei ⁡ ( x ) exponential-integral-Ei 𝑥 {\displaystyle{\displaystyle\mathrm{Ei}\left(\NVar{x}\right)}}
    xml-id
    C6.S2.SS1.p3.m2acdec
    0 references
    hyperbolic cosine integral
    Defining formula
    Chi ⁡ ( z ) hyperbolic-cosine-integral 𝑧 {\displaystyle{\displaystyle\mathrm{Chi}\left(\NVar{z}\right)}}
    xml-id
    C6.S2.E16.m2adec
    0 references
    imaginary unit
    Defining formula
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2acdec
    0 references
    Q11307
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C6.S1.XMD1.m1cdec
    0 references
     
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