# 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: v : float Order of the Lambda function x : float Value at which to evaluate the function and derivatives 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

 [R482] 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

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