DLMF:7.12.E4 (Q2415): 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
 
test:

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.m2acdec
Property / Symbols used
 
Property / Symbols used: Q11312 / rank
 
Normal rank
Property / Symbols used: Q11312 / qualifier
 
test:

z 𝑧 {\displaystyle{\displaystyle z}}

z
Property / Symbols used: Q11312 / qualifier
 
xml-id: C7.S1.XMD2.m1cdec
Property / Symbols used
 
Property / Symbols used: Q11314 / rank
 
Normal rank
Property / Symbols used: Q11314 / qualifier
 
test:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11314 / qualifier
 
xml-id: C7.S1.XMD3.m1dec

Latest revision as of 00:50, 2 January 2020

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DLMF:7.12.E4
No description defined

    Statements

    test
    f ⁡ ( z ) = 1 π ⁢ z ⁢ ∑ m = 0 n - 1 ( - 1 ) m ⁢ ( 1 2 ) 2 ⁢ m ( π ⁢ z 2 / 2 ) 2 ⁢ m + R n ( f ) ⁢ ( z ) , Fresnel-auxilliary-function-f 𝑧 1 𝜋 𝑧 superscript subscript 𝑚 0 𝑛 1 superscript 1 𝑚 Pochhammer 1 2 2 𝑚 superscript 𝜋 superscript 𝑧 2 2 2 𝑚 superscript subscript 𝑅 𝑛 Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(z\right)=\frac{1}{\pi z}\sum_{m=0}% ^{n-1}(-1)^{m}\frac{{\left(\tfrac{1}{2}\right)_{2m}}}{(\pi z^{2}/2)^{2m}}+R_{n% }^{(\mathrm{f})}(z),}}
    0 references
    DLMF id
    DLMF:7.12.E4
    0 references
    Symbols used
    auxiliary function for Fresnel integrals
    test
    f ⁡ ( z ) Fresnel-auxilliary-function-f 𝑧 {\displaystyle{\displaystyle\mathrm{f}\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E10.m2aadec
    0 references
    Q10759
    test
    ( a ) n Pochhammer 𝑎 𝑛 {\displaystyle{\displaystyle{\left(\NVar{a}\right)_{\NVar{n}}}}}
    xml-id
    C5.S2.SS3.m1acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q11312
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1cdec
    0 references
    Q11314
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1dec
    0 references
     
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