DLMF:7.6.E7 (Q2366)

From testwiki
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:7.6.E7
No description defined

    Statements

    test
    S ⁡ ( z ) = - cos ⁡ ( 1 2 ⁢ π ⁢ z 2 ) ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ π 2 ⁢ n + 1 1 ⋅ 3 ⁢ ⋯ ⁢ ( 4 ⁢ n + 3 ) ⁢ z 4 ⁢ n + 3 + sin ⁡ ( 1 2 ⁢ π ⁢ z 2 ) ⁢ ∑ n = 0 ∞ ( - 1 ) n ⁢ π 2 ⁢ n 1 ⋅ 3 ⁢ ⋯ ⁢ ( 4 ⁢ n + 1 ) ⁢ z 4 ⁢ n + 1 . Fresnel-sine-integral 𝑧 1 2 𝜋 superscript 𝑧 2 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝜋 2 𝑛 1 ⋅ 1 3 ⋯ 4 𝑛 3 superscript 𝑧 4 𝑛 3 1 2 𝜋 superscript 𝑧 2 superscript subscript 𝑛 0 superscript 1 𝑛 superscript 𝜋 2 𝑛 ⋅ 1 3 ⋯ 4 𝑛 1 superscript 𝑧 4 𝑛 1 {\displaystyle{\displaystyle S\left(z\right)=-\cos\left(\tfrac{1}{2}\pi z^{2}% \right)\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi^{2n+1}}{1\cdot 3\cdots(4n+3)}z^{4n% +3}+\sin\left(\tfrac{1}{2}\pi z^{2}\right)\sum_{n=0}^{\infty}\frac{(-1)^{n}\pi% ^{2n}}{1\cdot 3\cdots(4n+1)}z^{4n+1}.}}
    0 references
    DLMF id
    DLMF:7.6.E7
    0 references
    Symbols used
    Fresnel integral
    test
    S ⁡ ( z ) Fresnel-sine-integral 𝑧 {\displaystyle{\displaystyle S\left(\NVar{z}\right)}}
    xml-id
    C7.S2.E8.m2aadec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aedec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    sine function
    test
    sin ⁡ z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    xml-id
    C4.S14.E1.m2aadec
    0 references
    Q11312
    test
    z 𝑧 {\displaystyle{\displaystyle z}}
    xml-id
    C7.S1.XMD2.m1fdec
    0 references
    Q11314
    test
    n 𝑛 {\displaystyle{\displaystyle n}}
    xml-id
    C7.S1.XMD3.m1fdec
    0 references
     
      Retrieved from "https://lct.wmflabs.org/w/index.php?title=Item:Q2366&oldid=11696"