Computing limits for complex functions
in [HP48]
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From: Merciadri Luca on 6 Jun 2010 09:04 -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Hi, One can define sin(z), z being a complex number. How can the HP50g compute the limit of sin(z) when z approaches the positive infinity? (I.e. what could I type to achieve this?) I can evidently compute limits for real-valued functions, with the HP50g, but I never tried (and I don't know how to do it) with complex functions. Thanks. - -- Merciadri Luca See http://www.student.montefiore.ulg.ac.be/~merciadri/ - -- When you are courting a nice girl, an hour seems like a second. When you sit on a red-hot cinder, a second seems like an hour. That's relativity. (Albert Einstein) -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkwLnN0ACgkQM0LLzLt8MhzuAQCeIu4pLLZ9WP1km5lBZJGsr95a EwgAmgLm083dcNoNd+QScunUJy7KWNWU =SE9o -----END PGP SIGNATURE-----
From: Virgil on 6 Jun 2010 19:20 In article <87k4qcb9cx.fsf(a)merciadriluca-station.MERCIADRILUCA>, Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote: > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA1 > > Hi, > > One can define sin(z), z being a complex number. How can the HP50g > compute the limit of sin(z) when z approaches the positive infinity? Along what path? As far as I can see, there is no Z path towards positive real infinity along which SIN(Z) would even have a limit. > (I.e. what could I type to achieve this?) I can evidently compute > limits for real-valued functions, with the HP50g, but I never tried > (and I don't know how to do it) with complex functions.
From: Merciadri Luca on 7 Jun 2010 08:18 -----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Virgil <Virgil(a)home.esc> writes: > In article <87k4qcb9cx.fsf(a)merciadriluca-station.MERCIADRILUCA>, > Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote: > >> -----BEGIN PGP SIGNED MESSAGE----- >> Hash: SHA1 >> >> Hi, >> >> One can define sin(z), z being a complex number. How can the HP50g >> compute the limit of sin(z) when z approaches the positive infinity? > > Along what path? > > As far as I can see, there is no Z path towards positive real infinity > along which SIN(Z) would even have a limit. Sorry, I forgot to mention that this is not z, but |z|, and for |(sin(z))/[(z^2 + a^2)^2]|. But if I take a correct limit (i.e. one which exists), how can I compute it with the 50g? > >> (I.e. what could I type to achieve this?) I can evidently compute >> limits for real-valued functions, with the HP50g, but I never tried >> (and I don't know how to do it) with complex functions. - -- Merciadri Luca See http://www.student.montefiore.ulg.ac.be/~merciadri/ - -- A thief thinks everyone steals. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkwM44gACgkQM0LLzLt8MhzRdQCePScQrwpO8CP5oS5/YFL8AVNT 2XcAnA+CznGYlHZfZX1pFgV8Rot6nJ7A =q4QJ -----END PGP SIGNATURE-----
From: Virgil on 8 Jun 2010 02:12 In article <87typf11fa.fsf(a)merciadriluca-station.MERCIADRILUCA>, Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote: > -----BEGIN PGP SIGNED MESSAGE----- > Hash: SHA1 > > Virgil <Virgil(a)home.esc> writes: > > > In article <87k4qcb9cx.fsf(a)merciadriluca-station.MERCIADRILUCA>, > > Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote: > > > >> -----BEGIN PGP SIGNED MESSAGE----- > >> Hash: SHA1 > >> > >> Hi, > >> > >> One can define sin(z), z being a complex number. How can the HP50g > >> compute the limit of sin(z) when z approaches the positive infinity? > > > > Along what path? > > > > As far as I can see, there is no Z path towards positive real infinity > > along which SIN(Z) would even have a limit. > Sorry, I forgot to mention that this is not z, but |z|, and for > |(sin(z))/[(z^2 + a^2)^2]|. But if I > take a correct limit (i.e. one which exists), how can I compute it > with the 50g? > > > >> (I.e. what could I type to achieve this?) I can evidently compute > >> limits for real-valued functions, with the HP50g, but I never tried > >> (and I don't know how to do it) with complex functions. If the limit exists at all, it will exist along every complex path from z = 0 to |z| = oo. So to start with try it along each of the paths from 0 towards oo along one of the axial directions of the complex plane: t, -t, i*t and -i*t as real t goes towards oo. For each of those, you can work out explicit real expressions for |(sin(z))/[(z^2 + a^2)^2]| If all 4 have limits and are equal then there may actually be a limit for arbitrary paths
From: Merciadri Luca on 8 Jun 2010 07:44
-----BEGIN PGP SIGNED MESSAGE----- Hash: SHA1 Virgil <Virgil(a)home.esc> writes: > In article <87typf11fa.fsf(a)merciadriluca-station.MERCIADRILUCA>, > Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote: > >> -----BEGIN PGP SIGNED MESSAGE----- >> Hash: SHA1 >> >> Virgil <Virgil(a)home.esc> writes: >> >> > In article <87k4qcb9cx.fsf(a)merciadriluca-station.MERCIADRILUCA>, >> > Merciadri Luca <Luca.Merciadri(a)student.ulg.ac.be> wrote: >> > >> >> -----BEGIN PGP SIGNED MESSAGE----- >> >> Hash: SHA1 >> >> >> >> Hi, >> >> >> >> One can define sin(z), z being a complex number. How can the HP50g >> >> compute the limit of sin(z) when z approaches the positive infinity? >> > >> > Along what path? >> > >> > As far as I can see, there is no Z path towards positive real infinity >> > along which SIN(Z) would even have a limit. >> Sorry, I forgot to mention that this is not z, but |z|, and for >> |(sin(z))/[(z^2 + a^2)^2]|. But if I >> take a correct limit (i.e. one which exists), how can I compute it >> with the 50g? >> > >> >> (I.e. what could I type to achieve this?) I can evidently compute >> >> limits for real-valued functions, with the HP50g, but I never tried >> >> (and I don't know how to do it) with complex functions. > > If the limit exists at all, it will exist along every complex path from > z = 0 to |z| = oo. > > So to start with try it along each of the paths from 0 towards oo along > one of the axial directions of the complex plane: > t, -t, i*t and -i*t as real t goes towards oo. > For each of those, you can work out explicit real expressions for > |(sin(z))/[(z^2 + a^2)^2]| > > If all 4 have limits and are equal then there may actually be a limit > for arbitrary paths Yes, but I thought that the HP50g could have been able to try for all the axial directions of C^2! Thanks. - -- Merciadri Luca See http://www.student.montefiore.ulg.ac.be/~merciadri/ - -- Everyone wants to go to heaven, but no one wants to die. -----BEGIN PGP SIGNATURE----- Version: GnuPG v1.4.9 (GNU/Linux) Comment: Processed by Mailcrypt 3.5.8 <http://mailcrypt.sourceforge.net/> iEYEARECAAYFAkwOLR8ACgkQM0LLzLt8MhzZLwCdEj4umhu5EBXySbUcRO6H0Ead a/kAn059El31EEgq4tcG5ZZ7SUHOXD7E =LJ8Q -----END PGP SIGNATURE----- |