DLMF:7.6.E2 (Q2361): 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
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.m2aadec
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
Property / Symbols used
 
Property / Symbols used: Q11312 / rank
 
Normal rank
Property / Symbols used: Q11312 / qualifier
 
Defining formula:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11312 / qualifier
 
xml-id: C7.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11314 / rank
 
Normal rank
Property / Symbols used: Q11314 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11314 / qualifier
 
xml-id: C7.S1.XMD3.m1adec

Latest revision as of 01:41, 2 January 2020

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DLMF:7.6.E2
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    Statements

    erf z = 2 π e - z 2 n = 0 2 n z 2 n + 1 1 3 ( 2 n + 1 ) , error-function 𝑧 2 𝜋 superscript 𝑒 superscript 𝑧 2 superscript subscript 𝑛 0 superscript 2 𝑛 superscript 𝑧 2 𝑛 1 1 3 2 𝑛 1 {\displaystyle{\displaystyle\operatorname{erf}z=\frac{2}{\sqrt{\pi}}e^{-z^{2}}% \sum_{n=0}^{\infty}\frac{2^{n}z^{2n+1}}{1\cdot 3\cdots(2n+1)},}}
    0 references
    DLMF:7.6.E2
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    erf z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    C7.S2.E1.m2aadec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2adec
    0 references
    z 𝑧 {\displaystyle{\displaystyle z}}
    C7.S1.XMD2.m1adec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C7.S1.XMD3.m1adec
    0 references