Fourier analysis notation - Sh and Ch
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I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!
notation fourier-analysis
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I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!
notation fourier-analysis
2
My money's on hyperbolic sine and cosine.
â user1337
Jun 21 '15 at 8:45
This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
â Claude Leibovici
Jun 21 '15 at 8:47
Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
â Yves Daoust
Jun 21 '15 at 8:47
add a comment |Â
up vote
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down vote
favorite
up vote
0
down vote
favorite
I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!
notation fourier-analysis
I reading something dealing with Fourier analysis and don't know what "Sh" and "Ch" indicate. Thanks!
notation fourier-analysis
notation fourier-analysis
edited Jun 21 '15 at 10:07
wythagoras
21.4k442103
21.4k442103
asked Jun 21 '15 at 8:44
wellfedgremlin
367119
367119
2
My money's on hyperbolic sine and cosine.
â user1337
Jun 21 '15 at 8:45
This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
â Claude Leibovici
Jun 21 '15 at 8:47
Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
â Yves Daoust
Jun 21 '15 at 8:47
add a comment |Â
2
My money's on hyperbolic sine and cosine.
â user1337
Jun 21 '15 at 8:45
This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
â Claude Leibovici
Jun 21 '15 at 8:47
Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
â Yves Daoust
Jun 21 '15 at 8:47
2
2
My money's on hyperbolic sine and cosine.
â user1337
Jun 21 '15 at 8:45
My money's on hyperbolic sine and cosine.
â user1337
Jun 21 '15 at 8:45
This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
â Claude Leibovici
Jun 21 '15 at 8:47
This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
â Claude Leibovici
Jun 21 '15 at 8:47
Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
â Yves Daoust
Jun 21 '15 at 8:47
Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
â Yves Daoust
Jun 21 '15 at 8:47
add a comment |Â
1 Answer
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The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.
$$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$
$$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$
They are odd and even linear combinations of the exponential, so they easily appear with the latter.
Their name stems form the relation
$$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to
$$c^2+s^2=1$$ for the circular functions.
add a comment |Â
1 Answer
1
active
oldest
votes
1 Answer
1
active
oldest
votes
active
oldest
votes
active
oldest
votes
up vote
0
down vote
The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.
$$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$
$$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$
They are odd and even linear combinations of the exponential, so they easily appear with the latter.
Their name stems form the relation
$$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to
$$c^2+s^2=1$$ for the circular functions.
add a comment |Â
up vote
0
down vote
The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.
$$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$
$$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$
They are odd and even linear combinations of the exponential, so they easily appear with the latter.
Their name stems form the relation
$$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to
$$c^2+s^2=1$$ for the circular functions.
add a comment |Â
up vote
0
down vote
up vote
0
down vote
The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.
$$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$
$$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$
They are odd and even linear combinations of the exponential, so they easily appear with the latter.
Their name stems form the relation
$$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to
$$c^2+s^2=1$$ for the circular functions.
The hyperbolic functions are the "real" counterparts of the ordinary trigonometric ones.
$$textch(x)=cosh(x)=frace^x+e^-x2leftrightarrow cos(x)=frace^ix+e^-ix2,$$
$$textsh(x)=sinh(x)=frace^x-e^-x2leftrightarrow sin(x)=frace^ix-e^-ix2i.$$
They are odd and even linear combinations of the exponential, so they easily appear with the latter.
Their name stems form the relation
$$c^2-s^2=1$$ that corresponds to an hyperbola, to be compared to
$$c^2+s^2=1$$ for the circular functions.
edited Jun 22 '15 at 10:05
answered Jun 21 '15 at 8:55
Yves Daoust
114k665209
114k665209
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2
My money's on hyperbolic sine and cosine.
â user1337
Jun 21 '15 at 8:45
This was how we used to write $sinh$ and $cosh$ in France when I was young (looong time ago).
â Claude Leibovici
Jun 21 '15 at 8:47
Also written $sinh$ and $cosh$, and Hyp Sin, Hyp Cos on some calculators.
â Yves Daoust
Jun 21 '15 at 8:47