The Special Function {{\rm M}\left(m,\,n,\,x\right)}

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1. Differential Equation[-]

The function {{\rm M}\left(m,\,n,\,x\right)} satisfies the differential equation
\displaystyle x{\frac {d^{2}}{d{x}^{2}}}y \left( x \right) + \left( n-x \right) {\frac {d}{dx}}y \left( x \right) -my \left( x \right) = 0.
All formulas on this page are valid under the condition that n is not an integer (special values for parameters can be entered at the bottom).

2. Derivative in Terms of Lower-Order Derivatives[+]

3. Expansion at 0[+]

4. Local Expansions at Singularities and at Infinity[-]

The differential equation above has 0 non-zero finite singular pointsA complex number z_0 is a singular point (or singularity of a linear ordinary differential equation with polynomial coefficients, if the leading coefficient of the equation vanishes at z_0..

4.1. Expansion at \infty [+]

5. Hypergeometric Representation[+]

6. Parameters[-]

The Kummer function {{\rm M}\left(m,\,n,\,x\right)} depends on the parameters m and n. The boxes below can be used to rename or instantiate these parameters.
p1 =  p2 =