DLMF:7.11.E5 (Q2407): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: complementary error function / rank
 
Normal rank
Property / Symbols used: complementary error function / qualifier
 
Defining formula:

erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}

\erfc@@{\NVar{z}}
Property / Symbols used: complementary error function / qualifier
 
xml-id: C7.S2.E2.m2abdec

Revision as of 01:49, 2 January 2020

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DLMF:7.11.E5
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    Statements

    Defining formula
    erfc ⁡ z = 1 π ⁢ e - z 2 ⁢ U ⁡ ( 1 2 , 1 2 , z 2 ) = z π ⁢ e - z 2 ⁢ U ⁡ ( 1 , 3 2 , z 2 ) . complementary-error-function 𝑧 1 𝜋 superscript 𝑒 superscript 𝑧 2 Kummer-confluent-hypergeometric-U 1 2 1 2 superscript 𝑧 2 𝑧 𝜋 superscript 𝑒 superscript 𝑧 2 Kummer-confluent-hypergeometric-U 1 3 2 superscript 𝑧 2 {\displaystyle{\displaystyle\operatorname{erfc}z=\frac{1}{\sqrt{\pi}}e^{-z^{2}% }U\left(\tfrac{1}{2},\tfrac{1}{2},z^{2}\right)=\frac{z}{\sqrt{\pi}}e^{-z^{2}}U% \left(1,\tfrac{3}{2},z^{2}\right).}}
    0 references
    DLMF id
    DLMF:7.11.E5
    0 references
    Symbols used
    Kummer confluent hypergeometric function
    Defining formula
    U ⁡ ( a , b , z ) Kummer-confluent-hypergeometric-U 𝑎 𝑏 𝑧 {\displaystyle{\displaystyle U\left(\NVar{a},\NVar{b},\NVar{z}\right)}}
    xml-id
    C13.S2.E6.m2adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2addec
    0 references
    complementary error function
    Defining formula
    erfc ⁡ z complementary-error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erfc}\NVar{z}}}
    xml-id
    C7.S2.E2.m2abdec
    0 references
     
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