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2. Gradshteyn and Ryzhik - Wikipedia

   en.wikipedia.org/wiki/Gradshteyn_and_Ryzhik

   The integrals are classified by numbers, which haven't changed from the fourth Russian up to the seventh English edition (the numbering in older editions as well as in the eighth English edition is not fully compatible). The book does not only contain the integrals, but also lists additional properties and related special functions.

3. Euclidean quantum gravity - Wikipedia

   en.wikipedia.org/wiki/Euclidean_quantum_gravity

   Path integrals in contrast have been used in mechanics since the end of the nineteenth century and is well known. [ citation needed ] In addition, the path-integral formalism is used both in classical and quantum physics so it might be a good starting point for unifying general relativity and quantum theories.

4. Residue (complex analysis) - Wikipedia

   en.wikipedia.org/wiki/Residue_(complex_analysis)

   Then, the residue at the point c is calculated as: ⁡ (,) = = = = using the results from contour integral of a monomial for counter clockwise contour integral around a point c. Hence, if a Laurent series representation of a function exists around c, then its residue around c is known by the coefficient of the ( z − c ) − 1 {\displaystyle ...

5. Lists of integrals - Wikipedia

   en.wikipedia.org/wiki/Lists_of_integrals

   Integration is the basic operation in integral calculus.While differentiation has straightforward rules by which the derivative of a complicated function can be found by differentiating its simpler component functions, integration does not, so tables of known integrals are often useful.

6. Fredholm integral equation - Wikipedia

   en.wikipedia.org/wiki/Fredholm_integral_equation

   and the problem is, given the continuous kernel function and the function , to find the function .. An important case of these types of equation is the case when the kernel is a function only of the difference of its arguments, namely (,) = (), and the limits of integration are ±∞, then the right hand side of the equation can be rewritten as a convolution of the functions and and therefore ...

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8. Ramanujan's master theorem - Wikipedia

   en.wikipedia.org/wiki/Ramanujan's_master_theorem

   Output Integral value or integral cannot be assigned a value Express the integrand as a power series. Transform the integrand's power series to a bracket series. Obtain the complexity index, formula parameters and series coefficient function. Complexity index is the number of integrand sums minus number of brackets.

9. Fredholm theory - Wikipedia

   en.wikipedia.org/wiki/Fredholm_theory

   In mathematics, Fredholm theory is a theory of integral equations. In the narrowest sense, Fredholm theory concerns itself with the solution of the Fredholm integral equation. In a broader sense, the abstract structure of Fredholm's theory is given in terms of the spectral theory of Fredholm operators and Fredholm kernels on Hilbert space.