Abstract
Integrals of the formEquationSource<m:math display='block'> <m:mrow> <m:mstyle displaystyle='true'> <m:mrow><m:mo>∫</m:mo> <m:mrow> <m:mi>R</m:mi><m:mrow><m:mo>[</m:mo> <m:mrow> <m:mi>t</m:mi><m:mo>,</m:mo><m:mtext> </m:mtext><m:msqrt> <m:mrow> <m:mi>P</m:mi><m:mrow><m:mo>(</m:mo> <m:mi>t</m:mi> <m:mo>)</m:mo></m:mrow></m:mrow> </m:msqrt> </m:mrow> <m:mo>]</m:mo></m:mrow></m:mrow> </m:mrow> </m:mstyle><m:mtext> </m:mtext><m:mi>d</m:mi><m:mi>t</m:mi><m:mo>,</m:mo></m:mrow> </m:math>]]</EquationSource><EquationSource Format="TEX"> <![CDATA[$$\int {R\left[ {t,\;\sqrt {P\left( t \right)} } \right]} \;dt, $$ d t, where P (t) is a polynomial of the third or fourth degree and R is a rational function, have the simplest algebraic integrands that can lead to nonelementary1 integrals. Equivalent integrals occur in trigonometric and other forms, in pure and applied mathematics. Such integrals are known as elliptic integrals because a special example of this type arose in the rectification of the arc of an ellipse.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
Author information
Authors and Affiliations
Rights and permissions
Copyright information
© 1954 Springer-Verlag Berlin Heidelberg
About this chapter
Cite this chapter
Byrd, P.F., Friedman, M.D. (1954). Introduction. In: Handbook of Elliptic Integrals for Engineers and Physicists. Die Grundlehren der Mathematischen Wissenschaften, vol 67. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-52803-3_1
Download citation
DOI: https://doi.org/10.1007/978-3-642-52803-3_1
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-642-52805-7
Online ISBN: 978-3-642-52803-3
eBook Packages: Springer Book Archive