DLMF:13.6.E7 (Q4394): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: error function / rank
 
Normal rank
Property / Symbols used: error function / qualifier
 
Defining formula:

erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}

\erf@@{\NVar{z}}
Property / Symbols used: error function / qualifier
 
xml-id: C7.S2.E1.m2adec

Revision as of 15:51, 2 January 2020

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DLMF:13.6.E7
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    Statements

    Defining formula
    M ⁡ ( 1 2 , 3 2 , - z 2 ) = π 2 ⁢ z ⁢ erf ⁡ ( z ) , Kummer-confluent-hypergeometric-M 1 2 3 2 superscript 𝑧 2 𝜋 2 𝑧 error-function 𝑧 {\displaystyle{\displaystyle M\left(\tfrac{1}{2},\tfrac{3}{2},-z^{2}\right)=% \frac{\sqrt{\pi}}{2z}\operatorname{erf}\left(z\right),}}
    0 references
    DLMF id
    DLMF:13.6.E7
    0 references
    Symbols used
    $$={{}_{1}F_{1}}\left(\NVar{a};\NVar{b};\NVar{z}\right)$$ Kummer confluent hypergeometric function
    Defining formula
    M ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-M 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle M\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E2.m2addec
    0 references
    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
    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2adec
    0 references
     
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