DLMF:2.5.E39 (Q815): 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: 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
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.m3ajdec
Property / Symbols used
 
Property / Symbols used: Q11005 / rank
 
Normal rank
Property / Symbols used: Q11005 / qualifier
 
Defining formula:

h ( x ) 𝑥 {\displaystyle{\displaystyle h(x)}}

h(x)
Property / Symbols used: Q11005 / qualifier
 
xml-id: C2.S5.XMD16.m1kdec
Property / Symbols used
 
Property / Symbols used: Q11014 / rank
 
Normal rank
Property / Symbols used: Q11014 / qualifier
 
Defining formula:

I j ( x ) subscript 𝐼 𝑗 𝑥 {\displaystyle{\displaystyle I_{j}(x)}}

I_{j}(x)
Property / Symbols used: Q11014 / qualifier
 
xml-id: C2.S5.XMD25.m1adec

Latest revision as of 17:06, 1 January 2020

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DLMF:2.5.E39
No description defined

    Statements

    I j ( x ) = 0 e - t h j ( x t ) d t , subscript 𝐼 𝑗 𝑥 superscript subscript 0 superscript 𝑒 𝑡 subscript 𝑗 𝑥 𝑡 𝑡 {\displaystyle{\displaystyle I_{j}(x)=\int_{0}^{\infty}e^{-t}h_{j}(xt)\mathrm{% d}t,}}
    0 references
    DLMF:2.5.E39
    0 references
    j = 1 , 2 𝑗 1 2 {\displaystyle{\displaystyle j=1,2}}
    0 references
    d x 𝑥 {\displaystyle{\displaystyle\mathrm{d}\NVar{x}}}
    C1.S4.SS4.m1ajdec
    0 references
    e {\displaystyle{\displaystyle\mathrm{e}}}
    C4.S2.E11.m2abdec
    0 references
    {\displaystyle{\displaystyle\int}}
    C1.S4.SS4.m3ajdec
    0 references
    h ( x ) 𝑥 {\displaystyle{\displaystyle h(x)}}
    C2.S5.XMD16.m1kdec
    0 references
    I j ( x ) subscript 𝐼 𝑗 𝑥 {\displaystyle{\displaystyle I_{j}(x)}}
    C2.S5.XMD25.m1adec
    0 references