DLMF:7.11.E6 (Q2408): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
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.m2adec

Revision as of 01:49, 2 January 2020

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DLMF:7.11.E6
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    Statements

    Defining formula
    C ⁡ ( z ) + i ⁢ S ⁡ ( z ) = z ⁢ M ⁡ ( 1 2 , 3 2 , 1 2 ⁢ π ⁢ i ⁢ z 2 ) = z ⁢ e π ⁢ i ⁢ z 2 / 2 ⁢ M ⁡ ( 1 , 3 2 , - 1 2 ⁢ π ⁢ i ⁢ z 2 ) . Fresnel-cosine-integral 𝑧 𝑖 Fresnel-sine-integral 𝑧 𝑧 Kummer-confluent-hypergeometric-M 1 2 3 2 1 2 𝜋 𝑖 superscript 𝑧 2 𝑧 superscript 𝑒 𝜋 𝑖 superscript 𝑧 2 2 Kummer-confluent-hypergeometric-M 1 3 2 1 2 𝜋 𝑖 superscript 𝑧 2 {\displaystyle{\displaystyle C\left(z\right)+iS\left(z\right)=zM\left(\tfrac{1% }{2},\tfrac{3}{2},\tfrac{1}{2}\pi iz^{2}\right)=ze^{\pi iz^{2}/2}M\left(1,% \tfrac{3}{2},-\tfrac{1}{2}\pi iz^{2}\right).}}
    0 references
    DLMF id
    DLMF:7.11.E6
    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.m2adec
    0 references
    Fresnel integral
    Defining formula
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2adec
    0 references
     
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