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Zur Berechnung von Wirbelverteilung und Auftrieb eines dünnen Unterschallprofils in zwei hintereinander angeordneten Flügelgittern bei kompressiblen Strömungen
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Book
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Chapter
Elliptic Integrals Resulting from Laplace Transformations
Finding the Laplace transform1 of products of Bessel functions2 often leads to the evaluation of elliptic integrals. We shall give here, however, only a short table of such integrals.
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Chapter
Introduction
Integrals of the form <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...
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Chapter
Integrals of the Elliptic Integrals
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Chapter
Miscellaneous Integrals and Formulas
While most of the integrals in the previous sections have at least one variable upper limit, both of the limits of integration of the integrals given here are fixed.
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Chapter
Reduction of Hyperbolic Integrands to Jacobian Elliptic Functions
In addition to the algebraic or trigonometric forms given in the foregoing sections, elliptic integrals encountered in practical problems may also involve hyperbolic integrands.
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Chapter
Erratum
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Chapter
Elliptic Integrals of the Third Kind
The incomplete elliptic integral of the third kind in Legendre’s canonical form is defined by <m:math display='block'> <m:mrow> <m:msup> <m:mr...
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Chapter
Hyperelliptic Integrals
If <m:math display='block'> <m:mrow> <m:mi>P</m:mi><m:mrow><m:mo>(</m:mo> <m:mi>τ</m:mi> <m:mo>)</m:mo></m:mrow><m:mo>=</m:mo><m:msub> <m:mi>a</m:mi> <m:mn>0</m:mn> </m:msub> <m:msup> <m:m...
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Chapter
Definitions and Fundamental Relations
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Chapter
Derivatives
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Chapter
Reduction of Trigonometric Integrands to Jacobian Elliptic Functions
Various elliptic integrals involving trigonometric integrands occur in many geometrical and physical problems. In order to evaluate a variety of these we again find it convenient to express them in terms of in...
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Chapter
Expansions in Series
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Chapter
Table of Integrals of Jacobian Elliptic Functions
In the foregoing sections, where elliptic integrals having diverse algebraic, trigonometric, and hyperbolic integrands were reduced to those involving elliptic functions, it is seen that certain standard integ...
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Chapter
Miscellaneous Elliptic Integrals Involving Trigonometric and Hyperbolic Integrands
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Chapter
Reduction of Algebraic Integrands to Jacobian Elliptic Functions
The most general elliptic integral encountered in practice may appear in the form 200.00
200.00 <m:math display='block'> <m:mrow> <m:mi>Γ</m:mi><m:mo>=</m:mo><m:mstyle disp... -
Chapter
Elliptic Integrals Resulting from Laplace Transformations
Finding the Laplace transform1 of products of Bessel functions2 often leads to the evaluation of elliptic integrals. We shall give here, however, only a short table of such integrals.
-
Book
-
Chapter
Miscellaneous Integrals and Formulas
While most of the integrals in the previous sections have at least one variable upper limit, both of the limits of integration of the integrals given here are fixed.
