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**Extra info for An introduction to the theory of superfluidity**

**Example text**

Thus any specific Taylor series of w(z) would be an element of w(z). To be able to properly work with the Taylor series, it is necessary to understand the effect of singularities. For example, the real function f(x) = 1+~2 is non-negative, infinitely differentiable and has the Taylor series expansion -l

5) CONTINUE C PREPARE GLOBAL MATRICES 7 10 C C C DO 1000 J=1,NNOD IF(KTYPE(J)' EG. 1)P(J, 1)=1. 2)P(J,2)=1. LT .. 00001)GOTO 100 DELTA=DATAN(Y(J)/X(J» DO 200 K=3,NNOD 100 KK=(K-1) /2 XK=KK C............ CALCULATE KTH TERM IN TAYLOR SERIES RR=1. DO 125 KT=1,KK XKT=KT 125 RR=RR*R/XKT KKK=K-l SIGN=(-1. 1'. C......... 2)GOTO 150 C... O. )P(J,K)=RR*DCOS~XK*DELTA) IF(SIGN. LT. O. )P(~K)=-RR*DSIN(XK*DELTA) 37 S(J)=VALUE(J) GOTO 200 C... O. O. K)=RR*DCOSeXK*DELTA) S(J)=VALUE(J) 200 CONTINUE 1000 CONTINUE C...........

T)! t)! t)! 1}.! 1}.! 1}.! 1jJ 1jJ 1jJ 1jJ t)! 1jJ 1jJ t)! 47 1. 88 35 where NNOD is the total number of nodal points on r. can be numbered and defined in the interior of Q Of course, nodes as this program generates a value fitting polynomial of order (NNOD/2-1). ANS. V(NNOD). quare matrtx solution subroutine (Brebbia. out z ::; 0) . DAT" OPEN 6, "COI1PlEX. ANS" C.............. USES COMP 1. COMP2, COl1P3 COMMON/BlK 1/X(51) COMMON/BlK 2/Y(51) COMMON/BlK 3/KTYPE(51) COMMON/BlK 4/VAlUE(51) COMMON/BLK 5/P(51,51) COMMON/BLK 6/S(51) COMMON/BlK 7/COEF(51) COMMON/BLK S/ARRAY(51,2) DOUBLE PRECISION X,Y,P,S,COEF,VALUE,ARRAY DOUBLE PRECISION R,RR, DELTA, XK,SIGN C ZERO All ARRAYS C C DO 5 1=1.