Record

RefNoAP/38/26
LevelItem
TitleUnpublished paper, 'Second memoir upon the determination of unknown functions that are involved under definite integrals' by Joaquim Gomes de Souza
Date25 April 1856
DescriptionDe Souza proposes to himself the problem of determining the function ϕ which ( f, F being given functions, and the limits α, β of the integration being also given) satisfies the equation ∫βαf(x, θ) ϕ (x + θ) dθ = Fx. He observes, that, unlike the methods employed in his former memoir, and the solutions there employed, which are quite rigorous, the methods of the present memoir depend upon developments into series, the strictness of which has been contested by some mathematicians ; but that passing over these difficulties, he has solved the famous problem, the solution of which has been vainly sought after for the last two hundred years, because on the above-mentioned equation depends the integration of the generally linear equation of any order whatever of two variables, and consequently the whole integral calculus.

Subject: Mathematics / Calculus

Received 25 April 1836. Communicated by Dr [William] Sharpey.

Written by de Souza at 29 Brompton Square, London.

Whilst the Royal Society declined to publish this paper in full, an abstract of the paper was published in volume 8 of the Proceedings of the Royal Society as 'On the determination of unknown functions that are involved under definite integrals'.
Extent125p
FormatManuscript
PhysicalDescriptionInk on paper
Digital imagesView item on Science in the Making
AccessStatusOpen
RelatedMaterialDOI: 10.1098/rspl.1856.0041
RelatedRecordAP/39/11
Fellows associated with this archive
CodePersonNameDates
NA7273Sharpey; William (1802 - 1880)1802 - 1880
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