chapter9 二阶线性常微分方程的级数解法.ppt

* 由于Bessel方程的系数很简单，所以直接解也容易。 * Matab GAMMA Gamma function. Y = GAMMA(X) evaluates the gamma function for each element of X. X must be real. The gamma function is defined as: gamma(x) = integral from 0 to inf of t^(x-1) exp(-t) dt. The gamma function interpolates the factorial function. For integer n, gamma(n+1) = n! (n factorial) = prod(1:n). Class support for input X: float: double, single See also gammaln, gammainc, psi. Overloaded methods: sym/gamma Reference page in Help browser doc gamma GAMMALN Logarithm of gamma function. Y = GAMMALN(X) computes the natural logarithm of the gamma function for each element of X. GAMMALN is defined as LOG(GAMMA(X)) and is obtained without computing GAMMA(X). Since the gamma function can range over very large or very small values, its logarithm is sometimes more useful. Class support for input X: float: double, single GAMMAINC Incomplete gamma function. Y = GAMMAINC(X,A) evaluates the incomplete gamma function for corresponding elements of X and A. X and A must be real and the same size (or either can be a scalar). A must also be non-negative. The incomplete gamma function is defined as: gammainc(x,a) = 1 ./ gamma(a) .* integral from 0 to x of t^(a-1) exp(-t) dt For any a=0, as x approaches infinity, gammainc(x,a) approaches 1. For small x and a, gammainc(x,a) ~= x^a, so gammainc(0,0) = 1. Y = GAMMAINC(X,A,TAIL) specifies the tail of the incomplete gamma function when X is non-negative. Choices are lower (the default) and upper. The upper incomplete gamma function is defined as 1 - gammainc(x,a). Warning: When X is negative, Y can be inaccurate for abs(X) A+1. Class support for inputs X,A: float: double, single Y = PSI(X) evaluates the psi function for each element of X. X must be real and nonnegative. SIZE(Y) is the same