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Further, your suggestion that MM "knows" how to perform this integral analytically and does so is an egregious error. The Fermi-Dirac integral of negative half order (used in your example) must also be done numerically (quick google search). Even the answer given by MM, a number and not an expression, suggests that it is not employing a symbolic solution, but is indeed switching to a numerical method

A) unrelated to sage: as I already said in my previous post, I'd be careful making all-out statements. (Even more so based on 'quick' google seraches). So once again, to falsify your claims:

[1] The Analytical Evaluation of the Half-Order Fermi-Dirac Integrals Jerry A. Selvaggi, and Jerry P. Selvaggi The Open Mathematics Journal, 2012, 5, 1-7

[2] Solutions to the Fermi-Dirac Integrals in Semiconductor Physics Using Polylogarithms M. Ulrich, W. Seng, P. Barnes Journal of Computational Electronics 1: 431–434, 2002

and several other papers.

From the preceeding, I guess it is quite clear, where or to whom to apply vocabulary like 'egregious'. Moreover, it is Ref. [2] which tells you that things work down even to y>-1. Just pls. read the papers before posting.

B) related to sage: MM is not '..programmed to recognize Fermi-Dirac integrals and respond accordingly..'. Basically it uses eqn. (5) of Ref. [2], which is a paper free to be read with results free to be used by anyone - also outside of academia. Obviously MM has simply cared to include this result into its code - while sage has not. As simple as that.

with my tail between my legs

C) related to this forum I like this forum because it tends to be free of such statements. Pls. keep it that way.

Further, your suggestion that MM "knows" how to perform this integral analytically and does so is an egregious error. The Fermi-Dirac integral of negative half order (used in your example) must also be done numerically (quick google search). Even the answer given by MM, a number and not an expression, suggests that it is not employing a symbolic solution, but is indeed switching to a numerical method

A) unrelated to sage: as I already said in my previous post, I'd be careful making all-out statements. (Even more so based on 'quick' google seraches). So once again, to falsify your claims:

[1] The Analytical Evaluation of the Half-Order Fermi-Dirac Integrals Jerry A. Selvaggi, and Jerry P. Selvaggi The Open Mathematics Journal, 2012, 5, 1-7

[2] Solutions to the Fermi-Dirac Integrals in Semiconductor Physics Using Polylogarithms M. Ulrich, W. Seng, P. Barnes Journal of Computational Electronics 1: 431–434, 2002

and several other papers.papers. You should also realize, that there is a difference between scientific papers, like the preceding, which have undergone peer review, and some unpublished and unrefereed 'notes', which pop up on the internet - like the one you point to @ nanohub.org

From the preceeding, I guess it is quite clear, where or to whom to apply vocabulary like 'egregious'. Moreover, it is Ref. [2] which tells you that things work down even to y>-1. Just pls. read the papers before posting.

B) related to sage: MM is not '..programmed to recognize Fermi-Dirac integrals and respond accordingly..'. Basically it uses eqn. (5) of Ref. [2], which is a paper free to be read with results free to be used by anyone - also outside of academia. Obviously MM has simply cared to include this result into its code - while sage has not. As simple as that.

with my tail between my legs

C) related to this forum I like this forum because it tends to be free of such statements. Pls. keep it that way.