DLMF:8.21.E1 (Q2722): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2adec

Revision as of 14:14, 2 January 2020

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English
DLMF:8.21.E1
No description defined

    Statements

    Defining formula
    ci ⁡ ( a , z ) ± i ⁢ si ⁡ ( a , z ) = e ± 1 2 ⁢ π ⁢ i ⁢ a ⁢ Γ ⁡ ( a , z ⁢ e ∓ 1 2 ⁢ π ⁢ i ) , plus-or-minus generalized-cosine-integral-ci 𝑎 𝑧 𝑖 generalized-sine-integral-si 𝑎 𝑧 superscript 𝑒 plus-or-minus 1 2 𝜋 𝑖 𝑎 incomplete-Gamma 𝑎 𝑧 superscript 𝑒 minus-or-plus 1 2 𝜋 𝑖 {\displaystyle{\displaystyle\mathrm{ci}\left(a,z\right)\pm i\mathrm{si}\left(a% ,z\right)=e^{\pm\frac{1}{2}\pi ia}\Gamma\left(a,ze^{\mp\frac{1}{2}\pi i}\right% ),}}
    0 references
    DLMF id
    DLMF:8.21.E1
    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
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
     
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