DLMF:7.6.E8 (Q2367): 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.m2afdec

Revision as of 01:42, 2 January 2020

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DLMF:7.6.E8
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    Statements

    Defining formula
    erf ⁡ z = 2 ⁢ z π ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ ( 𝗂 2 ⁢ n ( 1 ) ⁡ ( z 2 ) - 𝗂 2 ⁢ n + 1 ( 1 ) ⁡ ( z 2 ) ) , error-function 𝑧 2 𝑧 𝜋 superscript subscript 𝑛 0 superscript 1 𝑛 spherical-Bessel-I-1 2 𝑛 superscript 𝑧 2 spherical-Bessel-I-1 2 𝑛 1 superscript 𝑧 2 {\displaystyle{\displaystyle\operatorname{erf}z=\frac{2z}{\sqrt{\pi}}\sum_{n=0% }^{\infty}(-1)^{n}\left({\mathsf{i}^{(1)}_{2n}}\left(z^{2}\right)-{\mathsf{i}^% {(1)}_{2n+1}}\left(z^{2}\right)\right),}}
    0 references
    DLMF id
    DLMF:7.6.E8
    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.m2afdec
    0 references
     
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