Re: [Boost-bugs] [Boost C++ Libraries] #7029: Add trigamma function

Subject: Re: [Boost-bugs] [Boost C++ Libraries] #7029: Add trigamma function
From: Boost C++ Libraries (noreply_at_[hidden])
Date: 2014-11-03 19:04:22

#7029: Add trigamma function
-----------------------------------+--------------------------------------
  Reporter:  agribov_no_s_p_a_m@…  |      Owner:  johnmaddock
      Type:  Feature Requests      |     Status:  new
 Milestone:  To Be Determined      |  Component:  math
   Version:  Boost 1.49.0          |   Severity:  Not Applicable
Resolution:                        |   Keywords:  trigamma, digamma, gamma
-----------------------------------+--------------------------------------

Comment (by johnmaddock):

 Many thanks for the response,

 > But may I ask why the multiplication theorem is not used in the
 formulas? It seems to be a nice way to reduce the problem for large
 arguments instead of heaving to rely on Bernoulli coefficients.

 The Bernoulli expansion is pretty efficient, for example at double
 precision it requires recursion to x > 9, then just 9 Bernoulli terms to
 converge.

 I don't immediately see how the
 [http://functions.wolfram.com/GammaBetaErf/PolyGamma2/16/02/01/0002/

 argument multiplication formula] helps in this case - as each reduction in
 x results in 2 new polygamma functions.

 >As you asked for concrete use cases: I want to use it for the gradient
 and Hessian of the Dirichlet-Function and in this case I need the bigamma
 and trigamma function at the same time. Therefore I miss a way to just
 compute both at the same time as they should share some computations...

 I don't think there much overlap in terms of computation as digamma uses
 rational approximations for the evaluation.

-- 
Ticket URL: <https://svn.boost.org/trac/boost/ticket/7029#comment:9>
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