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Wronskian

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The Wronskian of a set of n functions phi_1, phi_2, ... is defined by

W(phi_1,...,phi_n)=|phi_1 phi_2 ... phi_n; phi_1^' phi_2^' ... phi_n^'; | | ... |; phi_1^((n-1)) phi_2^((n-1)) ... phi_n^((n-1))|.

If the Wronskian is nonzero in some region, the functions phi_i are linearly independent. If W=0 over some range, the functions are linearly dependent somewhere in the range.

See also

Abel's Differential Equation Identity, Gram Determinant, Hessian, Jacobian, Linearly Dependent Functions

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References

Gradshteyn, I. S. and Ryzhik, I. M. "Wronskian Determinants." §14.315 in Tables of Integrals, Series, and Products, 6th ed. San Diego, CA: Academic Press, p. 1069, 2000.Morse, P. M. and Feshbach, H. Methods of Theoretical Physics, Part I. New York: McGraw-Hill, pp. 524-525, 1953.

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Wronskian

Cite this as:

Weisstein, Eric W. "Wronskian." From MathWorld--A Wolfram Web Resource. https://mathworld.wolfram.com/Wronskian.html

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