FunctionAdvisor(specialize, math_function_1)

FunctionAdvisor(specialize, math_function_1(a, b, ..., z))

FunctionAdvisor(specialize, math_function_1, math_function_2)

FunctionAdvisor(specialize, math_function_1(a, b, ..., z), math_function_2)

The specialization can be requested for particular values of some or all of the function parameters.

Note the difference between using specialize and relate (see FunctionAdvisor/relate). The former computes the required restrictions on the function parameters while the latter only returns a result when it does not require additional constraints on the parameters involved.

The following is a specialization which cannot be obtained using the relate keyword.

Knowing the possible specialization of a function is useful when trying to express functions in terms of other functions. Typically, the conversion is not possible unless restrictions on the function parameters are imposed. To perform the transformation (conversion), use the output of the FunctionAdvisor command with convert and assuming. For example, to transform as in the previous example, all KummerU functions entering an expression try the following.

The following example specializes sin into the other mathematical functions.

While the previous specializations do not require restrictions on the function parameters, if you specialize more general functions into simpler ones, restrictions are necessary. For example, for the LegendreQ function you have the following.

assuming, convert/to_special_function, FunctionAdvisor, FunctionAdvisor/relate, FunctionAdvisor/topics, sin