@@ -774,21 +774,21 @@ def kvtilde(
774774
775775 # Prepare zk for vectorized computation
776776 zk = np .tile (z , (nterms , 1 )).T
777- zk [:, 0 ] = 1
777+ zk [:, 0 ] = 1.0
778778 zk = np .cumprod (zk , axis = 1 )
779779
780780 k = np .arange (nterms )
781- ak = 4 * nu ** 2 - (2 * k - 1 ) ** 2
782- ak [0 ] = 1
783- ak = np .cumprod (ak ) / (factorial (k ) * (8 ** k ))
781+ ak = 4.0 * nu ** 2 - (2.0 * k - 1.0 ) ** 2
782+ ak [0 ] = 1.0
783+ ak = np .cumprod (ak ) / (factorial (k ) * (8.0 ** k ))
784784
785785 # Handling potential non-finite values in ak
786786 if not np .all (np .isfinite (ak )):
787787 first_nonfinite = np .where (~ np .isfinite (ak ))[0 ][0 ]
788788 ak = ak [:first_nonfinite ]
789789 zk = zk [:, :first_nonfinite ]
790790
791- K = sqrt (np .pi / (2 * z )) * (np .dot (1.0 / zk , ak ))
791+ K = sqrt (np .pi / (2.0 * z )) * (np .dot (1.0 / zk , ak ))
792792 K = K .reshape (sizez )
793793
794794 return K
@@ -811,21 +811,21 @@ def ivtilde(
811811
812812 # Prepare zk for vectorized computation with alternating signs for each term
813813 zk = np .tile (- z , (nterms , 1 )).T
814- zk [:, 0 ] = 1
814+ zk [:, 0 ] = 1.0
815815 zk = np .cumprod (zk , axis = 1 )
816816
817817 k = np .arange (nterms )
818- ak = 4 * nu ** 2 - (2 * k - 1 ) ** 2
819- ak [0 ] = 1
820- ak = np .cumprod (ak ) / (factorial (k ) * (8 ** k ))
818+ ak = 4.0 * nu ** 2 - (2.0 * k - 1.0 ) ** 2
819+ ak [0 ] = 1.0
820+ ak = np .cumprod (ak ) / (factorial (k ) * (8.0 ** k ))
821821
822822 # Handling potential non-finite values in ak
823823 if not np .all (np .isfinite (ak )):
824824 first_nonfinite = np .where (~ np .isfinite (ak ))[0 ][0 ]
825825 ak = ak [:first_nonfinite ]
826826 zk = zk [:, :first_nonfinite ]
827827
828- I = 1 / sqrt (2 * z * np .pi ) * (np .dot (1.0 / zk , ak ))
828+ I = 1.0 / sqrt (2.0 * z * np .pi ) * (np .dot (1.0 / zk , ak ))
829829 I = I .reshape (sizez )
830830
831831 return I
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