<abstract xmlns="http://www.w3.org/1999/xhtml"><p>In this article, we are going to look at the convergence properties of the integral <inline-formula><alternatives><inline-graphic xmlns:xlink="http://www.w3.org/1999/xlink" xlink:href="graphic/j_auom-2021-0014_eq_001.png"></inline-graphic><math xmlns:mml="http://www.w3.org/1998/Math/MathML" display="inline"><mrow><mrow><msubsup><mo>∫</mo><mn>0</mn><mn>1</mn></msubsup><mrow><msup><mrow><mrow><mrow><mo>(</mo><mrow><mi>a</mi><mi>x</mi><mo>+</mo><mi>b</mi></mrow><mo>)</mo></mrow></mrow></mrow><mrow><mi>c</mi><mi>x</mi><mo>+</mo><mi>d</mi></mrow></msup><mi>d</mi><mi>x</mi></mrow></mrow></mrow></math><tex-math>\int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx}</tex-math></alternatives></inline-formula>, and express it in series form, where <italic>a, b, c</italic> and <italic>d</italic> are real parameters.</p></abstract>

In this article, we are going to look at the convergence properties of the integral ∫01(ax+b)cx+ddx\int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx}, and express it in series form, where a, b, c and d are real parameters.

Extension of the Sophomore’s Dream

Analele ştiinţifice ale Universităţii "Ovidius" Constanţa. Seria Matematică

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

{"article-title":"Extension of the Sophomore\u2019s Dream"}

In this article, we are going to look at the convergence properties of the integral ∫01(ax+b)cx+ddx\int_0^1 {{{\left( {ax + b} \right)}^{cx + d}}dx}, and...

Extension of the Sophomore’s Dream

Online veröffentlicht: 13. Apr. 2021

Seitenbereich: 211 - 218

Eingereicht: 02. Feb. 2020

Akzeptiert: 10. Apr. 2020

DOI: https://doi.org/10.2478/auom-2021-0014

Schlüsselwörter
Sophomore’s dream, upper incomplete gamma function

© 2021 Gábor Román, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Extension of the Sophomore’s Dream

Online veröffentlicht: 13. Apr. 2021

Seitenbereich: 211 - 218

Eingereicht: 02. Feb. 2020

Akzeptiert: 10. Apr. 2020

DOI: https://doi.org/10.2478/auom-2021-0014

SchlüsselwörterSophomore’s dream, upper incomplete gamma function

© 2021 Gábor Román, published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Schlüsselwörter
Sophomore’s dream, upper incomplete gamma function