DLMF:10.52.E5 (Q3753): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: modified spherical Bessel function / rank
 
Normal rank
Property / Symbols used: modified spherical Bessel function / qualifier
 
test:

𝗂 n ( 2 ) ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}

\modsphBesseli{2}{\NVar{n}}@{\NVar{z}}
Property / Symbols used: modified spherical Bessel function / qualifier
 
xml-id: C10.S47.E8.m2aadec

Revision as of 13:13, 2 January 2020

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DLMF:10.52.E5
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    Statements

    test
    𝗂 n ( 1 ) ⁡ ( z ) ∼ 𝗂 n ( 2 ) ⁡ ( z ) ∼ 1 2 ⁢ z - 1 ⁢ e z , asymptotically-equals spherical-Bessel-I-1 𝑛 𝑧 spherical-Bessel-I-2 𝑛 𝑧 asymptotically-equals 1 2 superscript 𝑧 1 superscript 𝑒 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{n}}\left(z\right)\sim{\mathsf{i% }^{(2)}_{n}}\left(z\right)\sim\tfrac{1}{2}z^{-1}e^{z},}}
    0 references
    DLMF id
    DLMF:10.52.E5
    0 references
    constraint
    | ph ⁡ z | ≤ 1 2 ⁢ π - δ ( < 1 2 ⁢ π ) phase 𝑧 annotated 1 2 𝜋 𝛿 absent 1 2 𝜋 {\displaystyle{\displaystyle|\operatorname{ph}z|\leq\tfrac{1}{2}\pi-\delta(<% \tfrac{1}{2}\pi)}}
    0 references
    Symbols used
    asymptotic equality
    test
    ∼ asymptotically-equals {\displaystyle{\displaystyle\sim}}
    xml-id
    C2.S1.E1.m2acdec
    0 references
    the ratio of the circumference of a circle to its diameter
    test
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2abdec
    0 references
    base of natural logarithm
    test
    e {\displaystyle{\displaystyle\mathrm{e}}}
    xml-id
    C4.S2.E11.m2abdec
    0 references
    Q10817
    test
    ph phase {\displaystyle{\displaystyle\operatorname{ph}}}
    xml-id
    C1.S9.E7.m1adec
    0 references
    modified spherical Bessel function
    test
    𝗂 n ( 1 ) ⁡ ( z ) spherical-Bessel-I-1 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(1)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E7.m2aadec
    0 references
    modified spherical Bessel function
    test
    𝗂 n ( 2 ) ⁡ ( z ) spherical-Bessel-I-2 𝑛 𝑧 {\displaystyle{\displaystyle{\mathsf{i}^{(2)}_{\NVar{n}}}\left(\NVar{z}\right)}}
    xml-id
    C10.S47.E8.m2aadec
    0 references
     
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