Fuchsian%20equation
(0.003 seconds)
1—10 of 499 matching pages
1: 30.2 Differential Equations
§30.2 Differential Equations
►§30.2(i) Spheroidal Differential Equation
… ► … ►The Liouville normal form of equation (30.2.1) is … ►§30.2(iii) Special Cases
…2: 15.10 Hypergeometric Differential Equation
§15.10 Hypergeometric Differential Equation
… ►
15.10.1
►This is the hypergeometric differential equation.
…
►
…
►The connection formulas for the principal branches of Kummer’s solutions are:
…
3: 31.2 Differential Equations
§31.2 Differential Equations
►§31.2(i) Heun’s Equation
►
31.2.1
.
…
►
§31.2(v) Heun’s Equation Automorphisms
… ►Composite Transformations
…4: 29.2 Differential Equations
§29.2 Differential Equations
►§29.2(i) Lamé’s Equation
… ►§29.2(ii) Other Forms
… ►Equation (29.2.10) is a special case of Heun’s equation (31.2.1).5: 32.2 Differential Equations
§32.2 Differential Equations
►§32.2(i) Introduction
►The six Painlevé equations – are as follows: … ►§32.2(ii) Renormalizations
… ► …6: 28.2 Definitions and Basic Properties
…
►
§28.2(i) Mathieu’s Equation
… ►
28.2.1
…
►This is the characteristic equation of Mathieu’s equation (28.2.1).
…
►
§28.2(iv) Floquet Solutions
… ► …7: 28.20 Definitions and Basic Properties
…
►
§28.20(i) Modified Mathieu’s Equation
►When is replaced by , (28.2.1) becomes the modified Mathieu’s equation: ►
28.20.1
…
►
28.20.2
.
…
►Then from §2.7(ii) it is seen that equation (28.20.2) has independent and unique solutions that are asymptotic to as in the respective sectors , being an arbitrary small positive constant.
…
8: 31.14 General Fuchsian Equation
§31.14 General Fuchsian Equation
►§31.14(i) Definitions
►The general second-order Fuchsian equation with regular singularities at , , and at , is given by … ►Normal Form
… ►An algorithm given in Kovacic (1986) determines if a given (not necessarily Fuchsian) second-order homogeneous linear differential equation with rational coefficients has solutions expressible in finite terms (Liouvillean solutions). …9: Ranjan Roy
…
►Roy has published many papers on differential equations, fluid mechanics, special functions, Fuchsian groups, and the history of mathematics.
…
10: 31.15 Stieltjes Polynomials
…
►