DLMF:10.64.E2 (Q3830): Difference between revisions

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Changed an Item: Add constraint
Changed an Item: Add constraint
 
(3 intermediate revisions by the same user not shown)
Property / Symbols used
 
Property / Symbols used: Q10771 / rank
 
Normal rank
Property / Symbols used: Q10771 / qualifier
 
Defining formula:

{\displaystyle{\displaystyle\int}}

\int
Property / Symbols used: Q10771 / qualifier
 
xml-id: C1.S4.SS4.m3aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
Defining formula:

sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2aadec
Property / Symbols used
 
Property / Symbols used: Q11429 / rank
 
Normal rank
Property / Symbols used: Q11429 / qualifier
 
Defining formula:

n 𝑛 {\displaystyle{\displaystyle n}}

n
Property / Symbols used: Q11429 / qualifier
 
xml-id: C10.S1.XMD2.m1adec
Property / Symbols used
 
Property / Symbols used: Q11435 / rank
 
Normal rank
Property / Symbols used: Q11435 / qualifier
 
Defining formula:

x 𝑥 {\displaystyle{\displaystyle x}}

x
Property / Symbols used: Q11435 / qualifier
 
xml-id: C10.S1.XMD4.m1adec

Latest revision as of 14:22, 2 January 2020

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DLMF:10.64.E2
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    Statements

    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:10.64.E2
    0 references
    bei ν ( x ) Kelvin-bei 𝜈 𝑥 {\displaystyle{\displaystyle\operatorname{bei}_{\NVar{\nu}}\left(\NVar{x}% \right)}}
    C10.S61.E1.m3adec
    0 references
    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2aadec
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1aadec
    0 references
    sinh z 𝑧 {\displaystyle{\displaystyle\sinh\NVar{z}}}
    C4.S28.E1.m2adec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2aadec
    0 references
    n 𝑛 {\displaystyle{\displaystyle n}}
    C10.S1.XMD2.m1adec
    0 references
    x 𝑥 {\displaystyle{\displaystyle x}}
    C10.S1.XMD4.m1adec
    0 references