## File: ChangeLog-5.17-special-functions

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maxima 5.44.0-2
 `123456789101112131415161718192021222324252627282930313233343536373839404142434445464748495051525354555657585960616263646566676869707172737475767778798081828384858687888990919293949596979899100101102103104105106107108109110111112113114115116117118119120121122123124125126127128129130131132133134135136137138139140141142143144145146147148149150151152153154155156157158159160161162163164165166167168169170171172173174175176177178179180181182183184185186187` `````` Maxima 5.17 change log for special functions Compiled 2008-12-08 by Dieter Kaiser -------------------------------------------------------------------------------- Extensions and changes to the Factorial function: Maxima User function: factorial(z) New Maxima User variable: factorial_expand - Complex float and complex bigfloat support added - Check for a negative integer or a real representation of an integer - Set \$factlim to the value 100,000 to avoid unintentional overflow - Implementation of mirror symmetry - Expand factorial(n+m) where m is an integer The expansion depends on the Maxima User variable \$factorial_expand. The functionality is comparable with the function minfactorial. But because the expansion is done by the simplifier we have no problems with nested expression. Related bugs: SF handling of large factorials SF minfactorial doesn't look inside "!" -------------------------------------------------------------------------------- Changes to General factorial: Maxima User function: genfact(x,y,z): - Adding tests for the arguments of genfact(x,y,z). The algorithm of genfact(x,y,z) only works for the following range of the arguments: x, y, z positive integer and z <= x and y <= x/z. The tests for this range of values have been added. For integer values beyond this range a Maxima error is thrown. For all other numbers Maxima returns a noun form. Related bug: SF  double factorial defn incorrect for noninteger operand -------------------------------------------------------------------------------- Implementation of Double factorial New Maxima User function: double_factorial(z) New Maxima User variable: factorial_expand double_factorial is a generalization of genfact(x,y,z) for real and complex values. For an integer argument to double_factorial the function genfact(x,y,z) is called. - Numerical evaluation for integer, real and complex values in float and bigfloat precision - Implementation of the derivative - Mirror symmetry - Maxima Error for even negative integer - When \$factorial_expand T expansion for factorial_double(2*k+z) and k an integer - Transformation to a Gamma function with \$makegamma Related bug: SF  double factorial defn incorrect for noninteger operand -------------------------------------------------------------------------------- Extensions and improvements of the Gamma function Maxima User function: gamma(z) New Maxima User variable: gamma_expand - Adding code to evaluate complex bigfloats using the routine cbffac. - Detect a float or bigfloat representation of a negative integer. - Adding a test to check an overflow in the numerical routine gamma-lanczos. - Adding code for autoloading cbffac in max_ext.lisp - Simplify gamma(z+n) when n an integer e.g. gamma(z+1) = n * gamma(z) gamma(z+2) = n * (z+1) * gamma(z) gamma(z-1) = - gamma(z) / (1-n) gamma(z-2) = gamma(z) / ((1-n) * (2-n)) - Do the extraction of the realpart and imagpart when we know we have a complex number. - Improved accuracy for float, bigfloat and complex bigfloat values. - reduce the default value of \$gammalim to 10,000 - \$gammalim and \$factlim now work indepently Related bugs: SF  gamma(250.0) returns non-number; gamma(-1.0) finite SF  Gamma ask for the sign of an expression -------------------------------------------------------------------------------- Implementation of the Incomplete Gamma function New Maxima User function: gamma_incomplete(a,z) The following features are implemented: - Evaluation for real and complex numbers in double float and bigfloat precision - Special values for gamma_incomplete(a,0) and gamma_incomplete(a,inf) - When \$gamma_expand T expand the following expressions: gamma_incomplete(0,z) gamma_incomplete(n+1/2) gamma_incomplete(1/2-n) gamma_incomplete(n,z) gamma_incomplete(-n,z) gamma_incomplete(a+n,z) gamma_incomplete(a-n,z) - Mirror symmetry - Derivative wrt the arguments a and z -------------------------------------------------------------------------------- Implementation of the Generalized Incomplete Gamma function New Maxima User function: gamma_incomplete_generalized(a,z1,z2) The following features are implemented: - Evaluation for real and complex numbers in double float and bigfloat precision - Special values for: gamma_incomplete_generalized(a,z1,0) gamma_incomplete_generalized(a,0,z2), gamma_incomplete_generalized(a,z1,inf) gamma_incomplete_generalized(a,inf,z2) gamma_incomplete_generalized(a,0,inf) gamma_incomplete_generalized(a,x,x) - When \$gamma_expand T and n an integer expand gamma_incomplete_generalized(a+n,z1,z2) - Implementation of Mirror symmetry - Derivative wrt the arguments a, z1 and z2 -------------------------------------------------------------------------------- Implementation of the Regularized Incomplete Gamma function New Maxima User function: gamma_incomplete_regularized(a,z) The following features are implemented: - Evaluation for real and complex numbers in double float and bigfloat precision - Special values for: gamma_incomplete_regularized(a,0) gamma_incomplete_regularized(0,z) gamma_incomplete_regularized(a,inf) - When \$gamma_expand T and n a positive integer expansions for gamma_incomplete_regularized(n+1/2,z) gamma_incomplete_regularized(1/2-n,z) gamma_incomplete_regularized(n,z) gamma_incomplete_regularized(a+n,z) gamma_incomplete_regularized(a-n,z) - Derivative wrt the arguments a and z - Implementation of Mirror symmetry -------------------------------------------------------------------------------- Implementation of the Logarithm of the Gamma function New Maxima User function: log_gamma(z). The following features are implemented: - Evaluation for real and complex values in float and bigfloat precision. - For positive integer values n transformation to log(factorial(n)). - Check for negative integers, float or bigfloat representation. - Simplify gamma_log(inf) -> inf -------------------------------------------------------------------------------- Extension and implementation of the Error functions New Maxima User functions: erf(z) erfc(z) erfc(z) erfi(z) erf_generalized(z1,z2) New Maxima User flag: erf_representation The following features are implemented: - Real and complex evaluation in double float and bigfloat precision. - For numerical evaluation in double float precision the slatec routine slatec:derf is called. In all other cases the numerical routines of the Incomplete Gamma function are called. - Specific values for zero, one, inf and minf - Implementation of mirror symmetry - Transform into a representation in terms of the Error function erf when erf_representation is T - Odd reflection symmetry is implemented for the Error function erf ``````