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Module y0

Module y0 

Source

Functionsยง

f_y0
Bessel of the second kind of order 0 (Y0)
y0_asympt ๐Ÿ”’
y0_asympt_fast ๐Ÿ”’
y0_asympt_hard ๐Ÿ”’
y0_near_zero ๐Ÿ”’
Generated by SageMath: Evaluates: Y0(x) = 2/pi*(euler_gamma + log(x/2))J0(x) - sum((-1)^m(x/2)^(2m)/(m!)^2sum(1+1/2 + โ€ฆ 1/m)) expressed as: Y0(x)=log(x)*W0(x) - Z0(x)
y0_near_zero_fast ๐Ÿ”’
Generated by SageMath: Evaluates: Y0(x) = 2/pi*(euler_gamma + log(x/2))J0(x) - sum((-1)^m(x/2)^(2m)/(m!)^2sum(1+1/2 + โ€ฆ 1/m)) expressed as: Y0(x)=log(x)*W0(x) - Z0(x)
y0_small_argument_fast ๐Ÿ”’
This method on small range searches for nearest zero or extremum. Then picks stored series expansion at the point end evaluates the poly at the point.
y0_small_argument_hard ๐Ÿ”’
y0_small_argument_moderate ๐Ÿ”’
This method on small range searches for nearest zero or extremum. Then picks stored series expansion at the point end evaluates the poly at the point.
y0_transient_area_fast ๐Ÿ”’
Path for transient area between 1.35 to 2.
y0_transient_area_hard ๐Ÿ”’
y0_transient_area_moderate ๐Ÿ”’
Path for transient area between 1.35 to 2.