DLMF:7.18.E2 (Q2452): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
Defining formula:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2aadec

Revision as of 01:53, 2 January 2020

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DLMF:7.18.E2
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    Statements

    Defining formula
    i n ⁢ erfc ⁡ ( z ) = ∫ z ∞ i n - 1 ⁢ erfc ⁡ ( t ) ⁢ d t = 2 π ⁢ ∫ z ∞ ( t - z ) n n ! ⁢ e - t 2 ⁢ d t . repeated-integral-complementary-error-function 𝑛 𝑧 superscript subscript 𝑧 repeated-integral-complementary-error-function 𝑛 1 𝑡 𝑡 2 𝜋 superscript subscript 𝑧 superscript 𝑡 𝑧 𝑛 𝑛 superscript 𝑒 superscript 𝑡 2 𝑡 {\displaystyle{\displaystyle\mathop{\mathrm{i}^{n}\mathrm{erfc}}\left(z\right)% =\int_{z}^{\infty}\mathop{\mathrm{i}^{n-1}\mathrm{erfc}}\left(t\right)\mathrm{% d}t=\frac{2}{\sqrt{\pi}}\int_{z}^{\infty}\frac{(t-z)^{n}}{n!}e^{-t^{2}}\mathrm% {d}t.}}
    0 references
    DLMF id
    DLMF:7.18.E2
    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
     
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