DLMF:10.64.E2 (Q3830)

From DRMF
Revision as of 14:22, 2 January 2020 by Admin (talk | contribs) (‎Changed an Item: Add constraint)
Jump to navigation Jump to search
No description defined
Language Label Description Also known as
English
DLMF:10.64.E2
No description defined

    Statements

    Defining formula
    bei n ⁡ ( x ⁢ 2 ) = ( - 1 ) n π ⁢ ∫ 0 π sin ⁡ ( x ⁢ sin ⁡ t - n ⁢ t ) ⁢ sinh ⁡ ( x ⁢ sin ⁡ t ) ⁢ d t . Kelvin-bei 𝑛 𝑥 2 superscript 1 𝑛 𝜋 superscript subscript 0 𝜋 𝑥 𝑡 𝑛 𝑡 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle\operatorname{bei}_{n}\left(x\sqrt{2}\right)=\frac% {(-1)^{n}}{\pi}\int_{0}^{\pi}\sin\left(x\sin t-nt\right)\sinh\left(x\sin t% \right)\mathrm{d}t.}}
    0 references
    DLMF id
    DLMF:10.64.E2
    0 references
    Symbols used
    Kelvin function
    Defining formula
    bei ν ⁡ ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    xml-id
    C10.S61.E1.m3adec
    0 references
    the ratio of the circumference of a circle to its diameter
    Defining formula
    π {\displaystyle{\displaystyle\pi}}
    xml-id
    C3.S12.E1.m2aadec
    0 references
    Q10770
    Defining formula
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    xml-id
    C1.S4.SS4.m1aadec
    0 references
    hyperbolic sine function
    Defining formula
    sinh ⁡ z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    xml-id
    C4.S28.E1.m2adec
    0 references
     
        Retrieved from "https://drmf-beta.wmflabs.org/index.php?title=Item:Q3830&oldid=46334"