DLMF:10.54.E2 (Q3760): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: imaginary unit / rank
 
Normal rank
Property / Symbols used: imaginary unit / qualifier
 
test:

i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}

\iunit
Property / Symbols used: imaginary unit / qualifier
 
xml-id: C1.S9.E1.m2adec

Revision as of 13:15, 2 January 2020

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DLMF:10.54.E2
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    Statements

    test
    𝗃 n ⁡ ( z ) = ( - i ) n 2 ⁢ ∫ 0 π e i ⁢ z ⁢ cos ⁡ θ ⁢ P n ⁡ ( cos ⁡ θ ) ⁢ sin ⁡ θ ⁢ d θ . spherical-Bessel-J 𝑛 𝑧 superscript 𝑖 𝑛 2 superscript subscript 0 𝜋 superscript 𝑒 𝑖 𝑧 𝜃 shorthand-Legendre-P-first-kind 𝑛 𝜃 𝜃 𝜃 {\displaystyle{\displaystyle\mathsf{j}_{n}\left(z\right)=\frac{(-i)^{n}}{2}% \int_{0}^{\pi}e^{iz\cos\theta}P_{n}\left(\cos\theta\right)\sin\theta\mathrm{d}% \theta.}}
    0 references
    DLMF id
    DLMF:10.54.E2
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    cosine function
    test
    cos ⁡ z 𝑧 {\displaystyle{\displaystyle\cos\NVar{z}}}
    xml-id
    C4.S14.E2.m2aadec
    0 references
    Q10770
    test
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2adec
    0 references
    imaginary unit
    test
    i imaginary-unit {\displaystyle{\displaystyle\mathrm{i}}}
    xml-id
    C1.S9.E1.m2adec
    0 references
     
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