scipy.special.lmbda

scipy.special.lmbda(v, x)

Jahnke-Emden Lambda function, Lambdav(x).

This function is defined as [R502],

\[\Lambda_v(x) = \Gamma(v+1) \frac{J_v(x)}{(x/2)^v},\]

where \(\Gamma\) is the gamma function and \(J_v\) is the Bessel function of the first kind.

Parameters:

v : float

Order of the Lambda function

x : float

Value at which to evaluate the function and derivatives

Returns:

vl : ndarray

Values of Lambda_vi(x), for vi=v-int(v), vi=1+v-int(v), …, vi=v.

dl : ndarray

Derivatives Lambda_vi’(x), for vi=v-int(v), vi=1+v-int(v), …, vi=v.

References

[R501]

Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f_src/special_functions/special_functions.html

[R502]

(1, 2) Jahnke, E. and Emde, F. “Tables of Functions with Formulae and Curves” (4th ed.), Dover, 1945