DLMF:2.5.E9 (Q785): Difference between revisions

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Property / Symbols used
 
Property / Symbols used: the ratio of the circumference of a circle to its diameter / rank
 
Normal rank
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
test:

π {\displaystyle{\displaystyle\pi}}

\cpi
Property / Symbols used: the ratio of the circumference of a circle to its diameter / qualifier
 
xml-id: C3.S12.E1.m2acdec
Property / Symbols used
 
Property / Symbols used: Q10811 / rank
 
Normal rank
Property / Symbols used: Q10811 / qualifier
 
test:

absent {\displaystyle{\displaystyle\Re}}

\realpart@@
Property / Symbols used: Q10811 / qualifier
 
xml-id: C1.S9.E2.m1aadec
Property / Symbols used
 
Property / Symbols used: sine function / rank
 
Normal rank
Property / Symbols used: sine function / qualifier
 
test:

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

\sin@@{\NVar{z}}
Property / Symbols used: sine function / qualifier
 
xml-id: C4.S14.E1.m2adec
Property / Symbols used
 
Property / Symbols used: Q10998 / rank
 
Normal rank
Property / Symbols used: Q10998 / qualifier
 
test:

f ( t ) = 1 / ( 1 + t ) 𝑓 𝑡 1 1 𝑡 {\displaystyle{\displaystyle f(t)=1/(1+t)}}

f(t)=1/(1+t)
Property / Symbols used: Q10998 / qualifier
 
xml-id: C2.S5.XMD9.m1dec

Latest revision as of 16:02, 1 January 2020

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DLMF:2.5.E9
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    Statements

    f ( 1 - z ) = π sin ( π z ) , Mellin-transform 𝑓 1 𝑧 𝜋 𝜋 𝑧 {\displaystyle{\displaystyle\mathscr{M}\mskip-3.0mu f\mskip 3.0mu \left(1-z% \right)=\frac{\pi}{\sin\left(\pi z\right)},}}
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    0 < z < 1 0 𝑧 1 {\displaystyle{\displaystyle 0<\Re z<1}}
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    ( f ) ( s ) Mellin-transform 𝑓 𝑠 {\displaystyle{\displaystyle\mathscr{M}\left(\NVar{f}\right)\left(\NVar{s}% \right)}}
    C1.S14.E32.m2afdec
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    π {\displaystyle{\displaystyle\pi}}
    C3.S12.E1.m2acdec
    0 references
    absent {\displaystyle{\displaystyle\Re}}
    C1.S9.E2.m1aadec
    0 references
    sin z 𝑧 {\displaystyle{\displaystyle\sin\NVar{z}}}
    C4.S14.E1.m2adec
    0 references
    f ( t ) = 1 / ( 1 + t ) 𝑓 𝑡 1 1 𝑡 {\displaystyle{\displaystyle f(t)=1/(1+t)}}
    C2.S5.XMD9.m1dec
    0 references