DLMF:7.2.E11 (Q2333): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: Fresnel integral / rank
 
Normal rank
Property / Symbols used: Fresnel integral / qualifier
 
Defining formula:

C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}

\Fresnelcosint@{\NVar{z}}
Property / Symbols used: Fresnel integral / qualifier
 
xml-id: C7.S2.E7.m2acdec
Property / Symbols used
 
Property / Symbols used: Fresnel integral / rank
 
Normal rank
Property / Symbols used: Fresnel integral / qualifier
 
Defining formula:

S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}

\Fresnelsinint@{\NVar{z}}
Property / Symbols used: Fresnel integral / qualifier
 
xml-id: C7.S2.E8.m2acdec
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.m2ahdec
Property / Symbols used
 
Property / Symbols used: cosine function / rank
 
Normal rank
Property / Symbols used: cosine function / qualifier
 
Defining formula:

cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}

\cos@@{\NVar{z}}
Property / Symbols used: cosine function / qualifier
 
xml-id: C4.S14.E2.m2abdec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2abdec
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.m1idec

Latest revision as of 01:37, 2 January 2020

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DLMF:7.2.E11
No description defined

    Statements

    Defining formula
    g ⁡ ( z ) = ( 1 2 - C ⁡ ( z ) ) ⁢ cos ⁡ ( 1 2 ⁢ π ⁢ z 2 ) + ( 1 2 - S ⁡ ( z ) ) ⁢ sin ⁡ ( 1 2 ⁢ π ⁢ z 2 ) . Fresnel-auxilliary-function-g 𝑧 1 2 Fresnel-cosine-integral 𝑧 1 2 𝜋 superscript 𝑧 2 1 2 Fresnel-sine-integral 𝑧 1 2 𝜋 superscript 𝑧 2 {\displaystyle{\displaystyle\mathrm{g}\left(z\right)=\left(\tfrac{1}{2}-C\left% (z\right)\right)\cos\left(\tfrac{1}{2}\pi z^{2}\right)+\left(\tfrac{1}{2}-S% \left(z\right)\right)\sin\left(\tfrac{1}{2}\pi z^{2}\right).}}
    0 references
    DLMF id
    DLMF:7.2.E11
    0 references
    Symbols used
    Fresnel integral
    Defining formula
    C ⁡ ( z ) Fresnel-cosine-integral 𝑧 {\displaystyle{\displaystyle C\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E7.m2acdec
    0 references
    Fresnel integral
    Defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2ahdec
    0 references
    cosine function
    Defining formula
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2abdec
    0 references
    sine function
    Defining formula
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2abdec
    0 references
    Q11312
    Defining formula
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1idec
    0 references
     
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