Correction: Kowalenko, V. Exact Values of the Gamma Function from Stirling’s Formula. Mathematics 2020, 8, 1058

Victor Kowalenko

doi:10.3390/math11092151

School of Mathematics and Statistics, The University of Melbourne, Parkville, VIC 3010, Australia

Mathematics2023, 11(9), 2151;https://doi.org/10.3390/math11092151

This article belongs to the Special Issue Special Functions with Applications to Mathematical Physics

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Error in Table 4

In the original publication [1], there was a mistake in Table 4 as published. The value of TS for

N = 30

is incorrect. The value should be “−52.07235660935681329352406137393

i

”. The corrected Table 4 appears below.

Table 4.

ln Γ (3 exp (i π / 2))

via (25) for various values of N.

Table 4.

ln Γ (3 exp (i π / 2))

via (25) for various values of N.

N	Quantity	Value
	$F (3 exp (i π / 2))$	−4.3427565915140719616112579569 − 0.4895612973931192354299251350522 $i$
	$S D_{0}^{S L} (3 exp (i π / 2))$	3.256206078642828367679816468 $\times 10^{- 9}$
	Combined	−4.3427565882578658829684295892 − 0.4895612973931192354299251350522 $i$
	TS	$0$
1	$R_{1}^{S L} (3 exp (i π / 2))$	$-$ 0.0278840894653691199321777792256 $i$
	Total	−4.3427565882578658829684295892 − 0.5174453868584883553621029142779 $i$
	TS	$0$ − 0.0278842394252900781377131527007 $i$
6	$R_{6}^{S L} (3 exp (i π / 2))$	$0$ − 1.8907874105339892863379255 $\times 10^{- 8} i$
	Total	−4.3427565882578658829684295892 − 0.51744555572628341890753115113225 $i$
	TS	$0$ − 0.0278842563298976281594154202028 $i$
9	$R_{9}^{S L} (3 exp (i π / 2))$	$0$ + 3.2562060786428283676798164 $\times 10^{- 9} i$
	Total	−4.3427565882578658829684295892 − 0.51744555572628341890753115113225 $i$
	TS	$0$ − 0.0278842691899612112195938305035 $i$
15	$R_{15}^{S L} (3 exp (i π / 2))$	$0$ + 1.0856797027741987814423624 $\times 10^{- 8} i$
	Total	−4.3427565882578658829684295892 − 0.51744555572628341890753115113225 $i$
	TS	$0$ − 52.07235660935681329352406137393 $i$
30	$R_{30}^{S L} (3 exp (i π / 2))$	$0$ + 52.044472351023649035874440121314 $i$
	Total	−4.3427565882578658829684295892 − 0.51744555572628341890753115113225 $i$
	TS	$0$ − 6.4908409843349435181620453 $\times 10^{25} i$
50	$R_{50}^{S L} (3 exp (i π / 2))$	$0$ + 6.4908409843349435181620453 $\times 10^{25} i$
	Total	−4.3427565882578658829684295892 − 0.51744555572628341890753115113225 $i$
	$ln Γ (3 exp (i π / 2))$	−4.3427565882578658829684295892 − 0.51744555572268341890753115113225 $i$

The author states that the scientific conclusions are unaffected. This correction was approved by the Academic Editor. The original publication has also been updated.

Reference

Kowalenko, V. Exact Values of the Gamma Function from Stirling’s Formula. Mathematics 2020, 8, 1058. [Google Scholar] [CrossRef]

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© 2023 by the author. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/).

Correction: Kowalenko, V. Exact Values of the Gamma Function from Stirling’s Formula. Mathematics 2020, 8, 1058

Error in Table 4

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