iterated integral sentence in Hindi
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- So the two iterated integrals are different.
- If the above integral of the absolute value is not finite, then the two iterated integrals may have different values.
- On the other hand, some conditions ensure that the two iterated integrals are equal even though the double integral need not exist.
- The first two integrals are iterated integrals with respect to two measures, respectively, and the third is an integral with respect to the product measure.
- In mathematics, the "'Retkes Identities "', named after Zolt�n Retkes, are one of the most efficient applications of the iterated integrals
- But sometimes the two iterated integrals exist when the double integral does not, and in some such cases the two iterated integrals are different numbers, i . e ., one has
- But sometimes the two iterated integrals exist when the double integral does not, and in some such cases the two iterated integrals are different numbers, i . e ., one has
- Under suitable conditions ( e . g ., if " f " is continuous ), then Fubini's theorem guarantees that this integral can be expressed as an equivalent iterated integral
- If " f " is the characteristic function of " E " then the two iterated integrals of " f " are defined and have different values 1 and 0.
- If the double integral exists, then it is equal to each of the two iterated integrals ( either " " or " " ) and one often computes it by computing either of the iterated integrals.
- If the double integral exists, then it is equal to each of the two iterated integrals ( either " " or " " ) and one often computes it by computing either of the iterated integrals.
- Here \ scriptstyle T ^ k [ 1 ] is the k-th iterated integral of the constant 1, that is \ scriptstyle x ^ k / k !, and we get the exponential series.
- Then Tonelli's theorem allows us to rewrite H�lder's inequality using iterated integrals : If & thinsp; and are-measurable } } real-or complex-valued functions on the Cartesian product, then
- More precisely, the Tonelli Hobson test states that if " & fnof; " is a real-valued measurable function on "'R "'2, and either of the two iterated integrals
- If the integral is not absolutely convergent, care is needed not to confuse the concepts of " multiple integral " and " iterated integral ", especially since the same notation is often used for either concept.
- Notice that, by convention, the double integral has two integral signs, and the triple integral has three; this is a notational convention which is convenient when computing a multiple integral as an iterated integral, as shown later in this article.
- Coordinate iterated integrals ( terms of the signature ) form a more subtle algebra of features that can describe a stream or path in an analogous way; they allow a definition of rough path and form a natural linear " basis " for continuous functions on paths.
- In calculus, interchange of the "'order of integration "'is a methodology that transforms iterated integrals ( or multiple integrals through the use of Fubini's theorem ) of functions into other, hopefully simpler, integrals by changing the order in which the integrations are performed.
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