Handbook of Elliptic Integrals for Engineers and Physicists
Engineers and physicists are more and more encountering integrations involving nonelementary integrals and higher transeendental functions. Such integrations frequently involve (not always in immediately re cognizable form) elliptic functions and ellipti
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MATHEMATISCH EN WISSENSCHAFT EN IN EINZELDARSTELLUNGEN MIT BESONDERER BERUCKSICHTIGUNG DER ANWENDUNGSGEBIETE HERAUSGEGEBEN VON
R. GRAMMEL · E. HüPF · H . HüPF · F. RELLICH F. K. SCHMIDT · B. L. V AN DER W AERDEN BAND LXVII
HANDBOOK OF ELLIPTIC INTEGRALS FOR ENGINEERS AND PHYSICISTS by
PAUL F. BYRD and
MORRIS D. FRIEDMAN
SPRINGER-VERLAG BERLIN HEIDELBERG GMBH
HANDBOOK OF ELLIPTIC INTEGRALS FOR ENGINEERS AND PHYSICISTS by
PAUL F. BYRD
Aeronautkai Resear1
1:
+ i [F (A, k') - E (A, k') + ;,1~~~~ :i:;-~], 1. 1 1, and rp is as given in 116.01.
Special Addition Formulas.
!
F(ff,k) +F(ß,k) ==K,
117.01
E({}, k) +E(ß, k)
117.02
=
E
( 11(C1.2, k) +11(k2 jCI. 2, k). J ll(rp,
l-
Cl. 2 ,
k) +ll(rp, k
-F(rp,k)
ifcotß=k'tan{}
+ k2 sintl sinß. = K
+~V (1- ~2)~:2- k2)
if 0 < k 2
0)
=
gU
=
g sn-1 (sm 1p, k)
1
.
=
g F(1p, k)
