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The Hypergeometric Functions are defined in Abramowitz and Stegun, Handbook of Mathematical Functions, Chapters 13 and 15.
Maxima has very limited knowledge of these functions. They
can be returned from function hgfred
.
Whittaker M function
M[k,u](z) = exp(-z/2)*z^(1/2+u)*M(1/2+u-k,1+2*u,z)
.
(A&S 13.1.32)
Whittaker W function. (A&S 13.1.33)
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
.
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.
Examples:
(%i1) hypergeometric([],[],x); (%o1) %e^x
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; (%o3) -x^3/504+3*x^2/56-3*x/7+1
Both double float and big float evaluation is supported:
(%i4) hypergeometric([5.1],[7.1 + %i],0.42); (%o4) 1.346250786375334 - 0.0559061414208204 %i (%i5) hypergeometric([5,6],[8], 5.7 - %i); (%o5) .007375824009774946 - .001049813688578674 %i (%i6) hypergeometric([5,6],[8], 5.7b0 - %i), fpprec : 30; (%o6) 7.37582400977494674506442010824b-3 - 1.04981368857867315858055393376b-3 %i
Next: Parabolic Cylinder Functions, Previous: Struve Functions, Up: Special Functions [Contents][Index]