Abstract
The Riemann integral applies only to bounded functions defined on compact intervals. This severe restriction can be relaxed by considering larger concepts of integrability.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
References
Barbălat, I.: Systèmes d’équations différentielles d’oscillations non-linéaires. Rev. Roum. Math. Pures Appl. 4, 267–270 (1959)
Levrie, P., Daems, W.: Evaluating the probability integral using Wallis’s product formula for \(\pi \). Am. Math. Mon. 116, 538–541 (2009)
Apostol, T.M.: An elementary view of Euler’s summation formula. Am. Math. Mon. 106(5), 409–418 (1999)
Boas, R.P.: Partial sums of infinite series and how they grow. Am. Math. Mon. 84, 237–258 (1977)
Lampret, V.: The Euler-Maclaurin and Taylor formulas: twin elementary derivations. Math. Mag. 74, 109–122 (2001)
Boas, R.P.: A Primer of Real Functions. The Carus Mathematical Monographs, vol. 13. Mathematical Association of America, Washington (1996)
Artin, E. (1931, 1964): The Gamma Function. Holt, Rinehart and Winston, New York. English translation of German original. Teubner, Einführung in die Theorie der Gammafunktion (1964)
Dutkay, D.E., Niculescu, C.P., Popovici, F.: A short proof of Stirling’s formula. Am. Math. Mon. 120, 733–736 (2013)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
Copyright information
© 2014 Springer India
About this chapter
Cite this chapter
Choudary, A.D.R., Niculescu, C.P. (2014). Improper Riemann Integrals. In: Real Analysis on Intervals. Springer, New Delhi. https://doi.org/10.1007/978-81-322-2148-7_10
Download citation
DOI: https://doi.org/10.1007/978-81-322-2148-7_10
Published:
Publisher Name: Springer, New Delhi
Print ISBN: 978-81-322-2147-0
Online ISBN: 978-81-322-2148-7
eBook Packages: Mathematics and StatisticsMathematics and Statistics (R0)