Problems with the Riemann tensor in general relativity

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The discussion centers on deriving the second order derivative in the context of the Riemann tensor in general relativity, specifically referencing equations (1), (2), (3), and (3.71). The user is seeking clarification on the correctness of equation (3) and its relationship to the second order derivative. There is uncertainty about how to proceed from the current understanding of equation (4) if equation (3) is indeed accurate. Additionally, the user notes that the explanation following equation (3.71) was unclear, which complicates their ability to derive the necessary results. The conversation emphasizes the need for precise derivations and clarity in mathematical expressions related to the Riemann tensor.
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Homework Statement
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Relevant Equations
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After Taylor expansion and using equations (2), I have no problem getting to equation (1). Now obviously I have to somehow use (3.71) ,which I do know how, to derive to express the second order derivative.
On the internet I found equation (3), and I have tried to understand where this comes from (4).
Is equation (3) correct, if yes, how am i supposed to contineu from what I have in (4). It should equal 3 times the secobd order derivative?

If equation (3) is not correct, any tips how to continue from what I have?
 
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The sentence after (3.71) was a little unclear. I meant that I do know how to derive (3.71) using equations (2).
 

Thread 'Help needed with Elliptic Integrals'

I want to find the solution to the integral ##\theta = \int_0^{\theta}\frac{du}{\sqrt{(c-u^2 +2u^3)}}## I can see that ##\frac{d^2u}{d\theta^2} = A +Bu+Cu^2## is a Weierstrass elliptic function, which can be generated from ##\Large(\normalsize\frac{du}{d\theta}\Large)\normalsize^2 = c-u^2 +2u^3## (A = 0, B=-1, C=3) So does this make my integral an elliptic integral? I haven't been able to find a table of integrals anywhere which contains an integral of this form so I'm a bit stuck. TerryW
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