Improper Integrals. Elliptic Integrals and Functions

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


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


Elliptic Function Beta Function Infinite Series Elliptic Integral Jacobian Elliptic Function 
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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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