lit
    JINRLIB

DWHIT - Mk,m(z)

C325

: T.Pomentale :

popaa c a pa

C325_1

z k,m.
C325_2 - pa.

:

: - COMPLEX FUNCTION
: - DWHIT
: - BEWW,BOUND1,TWHIT

:

W=DWHIT(AK,AM,Z), :

AK - (COMPLEX*16) oc k;
AM - (COMPLEX*16) oc m;
Z - (COMPLEX*16) oc z.

:

coc pao a [1] C325_2:

C325_3(1)
ε0= 1, εn= 2 p n pao 0,
C325_4

R0 = 1; R1 = (c-2a)/c; In - opoa cc.

p c (1) cc In(z/2) coc aop Gautschi [2]. popo, o o aop a opo a ca, oa co o (1), ooo oc ooc ε, pa a |z|/2, oopo c o cao oo, oopo po p caapoo pppoo ooo In aa aa co ac.

pao C325_2, a o:

C325_5(2)
op
C325_6(3)

S0(r) oa poo aopa Gautschi ([2], p.37), co pao a a oppoa .
pa (3) c po co pa a. cc aaoo coacoa co o cc I0(z/2), oo a, o, oopa ac opo (3), , c a o op -a aoo o p c pa.

B p aa aa oac, oop o poo cpoa, ooac, oo c (2) (3) po co.

c:

z = + iy,
m = m1 + im2,
k = k1 + ik2.
      popa  oac      oopa oac
    ----------------------------------------------------------
    I =0   0<= y <= 100  I   0<= y <= 50     50<= y <=100   I
    I                     I                                  I
    I m=0   0<= m <= 15   I     a             a        I
    I  2         1        I                                  I
    I k=0   0<= k <= 141  I   0<= k <= 21     10<= k <= 21   I
    I  1         2        I        2                2        I
    ---------------------------------------------------------I
    I =0   0<= y <= 10   I              a                I
    I m=0   0<= m <= 0.6  I              a                I
    I  1         2        I                                  I
    I k=0   0<= k <= 20   I           0<= k <= 6             I
    I  1         2        I                2                 I
    I--------------------------------------------------------I
    I =0  10<= y <= 50   I              a                I
    I m=0   0<= m <= 0.6  I              a                I
    I  1         2        I                                  I
    I k=0   0<= k <= 20   I           0<= k <= 13            I
    I  1         2        I                2                 I
    ---------------------------------------------------------I
    I y=0   0<= x <= 100  I  0<= x <= 5       5 <= x <=50    I
    I m=0   0<= m <= 15   I     a             a        I
    I  2         1        I                                  I
    I k=0   0<= k <= 90   I  0<= k <= 10      0 <= k <= 0.8  I
    I  2         1        I       1                 1        I
    I--------------------------------------------------------I
    I y=0   0<= x <= 100  I  0<= x <= 5       5 <= x <=100   I
    I m=0   0<= m <= 0,6  I  0<= m <= 0.4       a         I
    I  2         1        I       1                          I
    I k=0   0<= k <= 90   I  0<= k <= 10      0 <= k <= 0.8  I
    I  2         1        I       1                 1        I
    ----------------------------------------------------------
 

a popa a m1 = 0, 0 <= m2 <= 0.6,
0 <= k1 <= 100, k2 = 0 z=x+iy, :

      popa          oopa    oac
        ac
    ------------------------------------------------------------
    I      I    I      I      I   m   I           k        I
    I-----------------------------------------------------------
    I 0.01  I 0.5 I a  I a  I a  I       a         I
    I 0.1   I 0.1 I a  I a  I a  I       a         I
    I  1.   I  1. I a  I a  I a  I       a         I
    I 10.   I 10. I a  I a  I a  I   0 <= k <= 5.0    I
    I       I     I       I       I       I         1          I
    I 20.   I 20. I a  I a  I a  I   0 <= k <= 0.5    I
    I       I     I       I       I       I         1          I
    I 0.5   I  1. I a  I a  I a  I      a          I
    I 0.5   I  6. I a  I a  I a  I   0 <= k <= 60     I
    I       I     I       I       I       I         1          I
    I 0.5   I 10. I a  I a  I a  I   0 <= k <= 40     I
    I       I     I       I       I       I         1          I
    I 0.5   I 20. I a  I a  I a  I   0 <= k <= 10     I
    I       I     I       I       I       I         1          I
    I 0.5   I 50. I a  I a  I a  I   0 <= k <= 10     I
    I       I     I       I       I       I         1          I
    I -0.01 I 0.5.I a  I a  I a  I       a         I
    I -0.1  I 0.5.I a  I a  I a  I       a         I
    I -1.   I  1. I a  I a  I a  I       a         I
    I -10.  I 10. I a  I a  I a  I   0 <= k <= 40     I
    I       I     I       I       I       I         1          I
    I -20.  I 20. I a  I a  I a  I   0 <= k <= 10     I
    I       I     I       I       I       I         1          I
    I -50.  I 50. I a  I a  I a  I   0 <= k <= 6      I
    I       I     I       I       I       I         1          I
    ------------------------------------------------------------

:

popa c cooa oo oac, oop pop.
7 . c z=0 REAL(m)<-1/2, o aac cooca aoca.

:

  1. L.Luk, Epansion of the Conflunt Hprgeometric Function in Sries of Bssl Functions. Math. of Comp., 13, 1959, 261-271.
  2. W.Gautschi, Computational Aspcts of three-trm Rcurrnc Rlations. SIAM Rviw, 9, 1967, 24-82.


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