DLMF:7.6.E8 (Q2367): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: modified spherical Bessel function / rank
 
Normal rank
Property / Symbols used: modified spherical Bessel function / qualifier
 
Defining formula:

𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}

\modsphBesseli{1}{\NVar{n}}@{\NVar{z}}
Property / Symbols used: modified spherical Bessel function / qualifier
 
xml-id: C10.S47.E7.m2adec

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
    error function
    Defining formula
    erf ⁡ z error-function 𝑧 {\displaystyle{\displaystyle\operatorname{erf}\NVar{z}}}
    xml-id
    C7.S2.E1.m2abdec
    0 references
    modified spherical Bessel function
    Defining formula
    𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E7.m2adec
    0 references
     
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