1 | initial version |

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: 431434, 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.

2 | added comment on 'notes' from nanohub.org |

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: 431434, 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.

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