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)