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Generalization of Hermite polynomials for negative, fractional degree.

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#ordinary-differential-equations #polynomials #special-functions #hypergeometric-function #hermite-polynomials
91
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Special function $Z_r(x)$ in Plasma physics.

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#physics #special-functions
347
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Evaluate $\int_0^\infty \frac{x^2\operatorname{Ti}_2(x^2)}{x^4+1} \space dx$

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#integration #definite-integrals #improper-integrals #special-functions
365
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What are some methods to evaluate $ \int_{0}^{1} \frac{t^3 - 1}{\ln(t)} \, dt$?

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#calculus #definite-integrals #special-functions
86
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Solutions of 2nd order Fuchsian differential equations as Heun or Hypergeometric functions.

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#complex-analysis #ordinary-differential-equations #special-functions #hypergeometric-function
142
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How to prove Legendre Polynomials' recurrence relation without using explicit formula?

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#real-analysis #recurrence-relations #special-functions #orthogonal-polynomials #legendre-polynomials
195
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Weierstrass Zeta $\zeta(x;a,b)$ inverse

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#special-functions #closed-form #inverse-function #beta-function #elliptic-functions
76
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Could someone help prove some properties of Legendre Polynomials?

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#polynomials #special-functions #mathematical-physics #orthogonal-polynomials #legendre-polynomials
84
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Integral involving a complete elliptic integral $\int_0^1 dt \frac{K(t)}{\sqrt{t\left(t+\frac{z}{1-z}\right)}}$

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#integration #definite-integrals #special-functions #elliptic-integrals
90
Views

How to simplify RMM limit of integral?

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#analysis #definite-integrals #special-functions #hypergeometric-function #beta-function
193
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A log log integral

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#calculus #integration #definite-integrals #special-functions
97
Views

reference for Heun's differential equation

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#ordinary-differential-equations #special-functions
97
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How to find a closed form expression for the integral of an exponential divided by a polynomial over an infinite range?

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#integration #definite-integrals #taylor-expansion #special-functions #hypergeometric-function
119
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Equations reducible to Bessel's equation

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#ordinary-differential-equations #special-functions #bessel-functions
119
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Solve an improper integral with help of Basset's integral

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#calculus #improper-integrals #special-functions #fourier-transform

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