Evaluate numerically:

Plot over a subset of the reals:

Evaluate symbolically:

Series expansion at the origin:

Series expansion at Infinity:

Solve a differential equation of hypergeometric type:

Solve a third-order singular ODE in terms of the HypergeometricPFQ and MeijerG functions:

Verify that the components of the general solution for an ODE are linearly independent:

A formula for solutions to the trinomial equation :

First root of the quintic :

Check the solution:

Effective confining potential in random matrix theory for a Gaussian density of states:

Its series expansion at infinity reveals logarithmic growth:

An expression for the surface tension of an electrolyte solution as a function of concentration y:

Onsager–Samaras limiting law for very low concentrations:

Fractional derivative of Sin:

Derivative of order of Sin:

Plot a smooth transition between the derivative and integral of Sin:

Define the Gram polynomial in terms of HypergeometricPFQ:

Verify a discrete orthogonality relation satisfied by the Gram polynomials:

Use the Gram polynomial to compute the Savitzky–Golay smoothing coefficients:

Compare with the result of SavitzkyGolayMatrix:

Integrate frequently returns results containing HypergeometricPFQ:

Sum may return results containing HypergeometricPFQ:

Use FunctionExpand to transform HypergeometricPFQ into less general functions:

Machine-precision input may be insufficient to get a correct answer:

With exact input, the answer is correct:

Common symbolic parameters in HypergeometricPFQ generically cancel:

However, when there is a negative integer among common elements, HypergeometricPFQ is interpreted as a polynomial:

The period of an anharmonic oscillator with Hamiltonian :

Period for quartic anharmonicity:

Limit of pure quartic potential: