scipy.special.lmbda¶

scipy.special.lmbda(v, x)[source]¶

Jahnke-Emden Lambda function, Lambdav(x).

This function is defined as [R483],

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

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

Parameters:

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.

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

Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. http://jin.ece.illinois.edu/specfunc.html

[R483]

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