scipy.special.
lmbda#
- scipy.special.lmbda(v, x)[source]#
Jahnke-Emden Lambda function, Lambdav(x).
This function is defined as [2],
\[\Lambda_v(x) = \Gamma(v+1) \frac{J_v(x)}{(x/2)^v},\]where \(\Gamma\) is the gamma function and \(J_v\) is the Bessel function of the first kind.
- Parameters:
- vfloat
Order of the Lambda function
- xfloat
Value at which to evaluate the function and derivatives
- Returns:
- vlndarray
Values of Lambda_vi(x), for vi=v-int(v), vi=1+v-int(v), …, vi=v.
- dlndarray
Derivatives Lambda_vi’(x), for vi=v-int(v), vi=1+v-int(v), …, vi=v.
References
[1]Zhang, Shanjie and Jin, Jianming. “Computation of Special Functions”, John Wiley and Sons, 1996. https://people.sc.fsu.edu/~jburkardt/f77_src/special_functions/special_functions.html
[2]Jahnke, E. and Emde, F. “Tables of Functions with Formulae and Curves” (4th ed.), Dover, 1945