DLMF:10.54.E4 (Q3762): Difference between revisions

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‎Changed an Item: Add constraint
‎Changed an Item: Add constraint
Property / Symbols used
 
Property / Symbols used: base of natural logarithm / rank
 
Normal rank
Property / Symbols used: base of natural logarithm / qualifier
 
Defining formula:

e {\displaystyle{\displaystyle\mathrm{e}}}

\expe
Property / Symbols used: base of natural logarithm / qualifier
 
xml-id: C4.S2.E11.m2abdec

Revision as of 14:15, 2 January 2020

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DLMF:10.54.E4
No description defined

    Statements

    Defining formula
    𝗃 n ⁡ ( z ) = ( - i ) n + 1 2 ⁢ π ⁢ ∫ i ⁢ ∞ ( - 1 + , 1 + ) e i ⁢ z ⁢ t ⁢ Q n ⁡ ( t ) ⁢ d t , spherical-Bessel-J 𝑛 𝑧 superscript 𝑖 𝑛 1 2 𝜋 superscript subscript 𝑖 limit-from 1 limit-from 1 superscript 𝑒 𝑖 𝑧 𝑡 shorthand-Legendre-Q-second-kind 𝑛 𝑡 𝑡 {\displaystyle{\displaystyle\mathsf{j}_{n}\left(z\right)=\frac{(-i)^{n+1}}{2% \pi}\int_{i\infty}^{(-1+,1+)}e^{izt}Q_{n}\left(t\right)\mathrm{d}t,}}
    0 references
    DLMF id
    DLMF:10.54.E4
    0 references
    constraint
    | ph ⁡ z | < 1 2 ⁢ π . phase 𝑧 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|<\tfrac{1}{2}\pi.}}
    0 references
    Symbols used
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2acdec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1acdec
    0 references
    base of natural logarithm
    Defining formula
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
     
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