DLMF:8.11.E10 (Q2583): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Q11332 / rank
 
Normal rank
Property / Symbols used: Q11332 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11332 / qualifier
 
xml-id: C8.S1.XMD1.m1bdec

Revision as of 13:54, 2 January 2020

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DLMF:8.11.E10
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    Statements

    Defining formula
    P ⁡ ( a + 1 , x ) = 1 2 ⁢ erfc ⁡ ( - y ) - 1 3 ⁢ 2 π ⁢ a ⁢ ( 1 + y 2 ) ⁢ e - y 2 + O ⁡ ( a - 1 ) , incomplete-gamma-P 𝑎 1 𝑥 1 2 complementary-error-function 𝑦 1 3 2 𝜋 𝑎 1 superscript 𝑦 2 superscript 𝑒 superscript 𝑦 2 Big-O superscript 𝑎 1 {\displaystyle{\displaystyle P\left(a+1,x\right)=\tfrac{1}{2}\operatorname{% erfc}\left(-y\right)-\frac{1}{3}\sqrt{\frac{2}{\pi a}}(1+y^{2})e^{-y^{2}}+O% \left(a^{-1}\right),}}
    0 references
    DLMF id
    DLMF:8.11.E10
    0 references
    Symbols used
    order not exceeding
    Defining formula
    O ⁡ ( x ) Big-O 𝑥 {\displaystyle{\displaystyle O\left(\NVar{x}\right)}}
    xml-id
    C2.S1.E3.m2aadec
    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.m2adec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2aedec
    0 references
    Q11325
    Defining formula
    P ⁡ ( a , z ) incomplete-gamma-P 𝑎 𝑧 {\displaystyle{\displaystyle P\left(\NVar{a},\NVar{z}\right)}}
    xml-id
    C8.S2.E4.m1aadec
    0 references
    Q11332
    Defining formula
    x 𝑥 {\displaystyle{\displaystyle x}}
    xml-id
    C8.S1.XMD1.m1bdec
    0 references
     
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