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Improper Integrals. Elliptic Integrals and Functions

  • Emanuel Fischer
Part of the Undergraduate Texts in Mathematics book series (UTM)

Abstract

When f is R-integrable over [a, b] then its indefinite integral F, defined as
$$F\left( x \right) = \int_a^x {f\left( t \right)dt\,\,\,\,for\,\,\,\,x \in \left[ {a,b} \right]} ,$$
(1.1)
is continuous on [a,b] (Theorem XIII.6.3). Hence,
$$_{x \to b - }^{\lim }\int_a^x {f\left( t \right)dt = \int_a^b {f\left( t \right)dt.} }$$
(1.2)

Keywords

Elliptic Function Beta Function Infinite Series Elliptic Integral Jacobian Elliptic Function 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag New York, Inc. 1983

Authors and Affiliations

  • Emanuel Fischer
    • 1
  1. 1.Department of MathematicsAdelphi UniversityGarden CityUSA

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