Maxima – 104 – Funzioni speciali – 10

Continuo da qui, copio dal Reference Manual, PDF scaricabile da qui, sono a p.311.

Funzioni di Struve

The Struve functions are defined in Abramowitz and Stegun, Handbook of Mathematical Functions, Chapter 12, o la Wiki.

struve_h (v, z)
The Struve Function H of order v and argument z.

struve_l (v, z)
The Modified Struve Function L of order v and argument z.

Funzioni ipergeometriche

The Hypergeometric Functions are defined in Abramowitz and Stegun, Handbook of Matematical Functions, Chapters 13 and 15, o la Wiki.

Maxima has very limited knowledge of these functions. They can be returned from function hgfred.

%m [k,u] (z)
Whittaker M function M[k,u](z) = exp(-z/2)*z^(1/2+u)*M(1/2+u-k,1+2*u,z).

%w [k,u] (z)
Whittaker W function.

%f [p,q] ([a],[b],z)
The pFq(a1,a2,..ap;b1,b2,..bq;z) hypergeometric function, where a a list of length p and b a list of length q.

hypergeometric ([a1, ..., ap],[b1, ... ,bq], x)
The hypergeometric function. Unlike Maxima’s %f hypergeometric function, the function hypergeometric is a simplifying function; also, hypergeometric supports complex double and big floating point evaluation. For the Gauss hypergeometric function, that is p = 2 and q = 1, floating point evaluation outside the unit circle is supported, but in general, it is not supported.

When the option variable expand_hypergeometric is true (default is false) and one of the arguments a1 through ap is a negative integer (a polynomial case), hypergeometric returns an expanded polynomial.

(%i1) hypergeometric([],[],x);
                                        x
(%o1)                                 %e

Polynomial cases automatically expand when expand_hypergeometric is true:

(%i2) hypergeometric([-3],[7],x);
(%o2)                    hypergeometric([- 3], [7], x)
(%i3) hypergeometric([-3],[7],x), expand_hypergeometric : true;
                               3        2
                              x      3 x    3 x
(%o3)                      (- ---) + ---- - --- + 1
                              504     56     7

Both double float and big float evaluation is supported:

(%i4) hypergeometric([5.1],[7.1 + %i],0.42);
(%o4)              1.346250786375333 - 0.0559061414208204 %i
(%i5) hypergeometric([5,6],[8], 5.7 - %i);
(%o5)           0.007375824009774945 - 0.001049813688578673 %i
(%i6) hypergeometric([5,6],[8], 5.7b0 - %i), fpprec : 30;
(%o6) 7.37582400977494674506442010824b-3
                                        - 1.04981368857867315858055393376b-3 %i

Funzioni paraboliche del cilindro

The Parabolic Cylinder Functions are defined in Abramowitz and Stegun, Handbook of Mathematical Functions, Chapter 19, o la Wiki.

Maxima has very limited knowledge of these functions. They can be returned from function hgfred.

parabolic_cylinder_d (v, z)
The parabolic cylinder function.

Posta un commento o usa questo indirizzo per il trackback.

Trackback

Rispondi

Inserisci i tuoi dati qui sotto o clicca su un'icona per effettuare l'accesso:

Logo di WordPress.com

Stai commentando usando il tuo account WordPress.com. Chiudi sessione /  Modifica )

Google photo

Stai commentando usando il tuo account Google. Chiudi sessione /  Modifica )

Foto Twitter

Stai commentando usando il tuo account Twitter. Chiudi sessione /  Modifica )

Foto di Facebook

Stai commentando usando il tuo account Facebook. Chiudi sessione /  Modifica )

Connessione a %s...

Questo sito utilizza Akismet per ridurre lo spam. Scopri come vengono elaborati i dati derivati dai commenti.

%d blogger hanno fatto clic su Mi Piace per questo: