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1: 19.7 Connection Formulas
§19.7(ii) Change of Modulus and Amplitude
2: 29.2 Differential Equations
29.2.5 ϕ = 1 2 π - am ( z , k ) .
3: 29.1 Special Notation
where ψ = am ( z , k ) ; see §22.16(i). The relation to the Lamé functions Ec ν m , Es ν m of Ince (1940b) is given by …
4: 29.6 Fourier Series
With ϕ = 1 2 π - am ( z , k ) , as in (29.2.5), we have …
5: Errata
Changes
Changes
Changes
Changes
Changes
6: 19.25 Relations to Other Functions
then the five nontrivial permutations of x , y , z that leave R F invariant change k 2 ( = ( z - y ) / ( z - x ) ) into 1 / k 2 , k 2 , 1 / k 2 , - k 2 / k 2 , - k 2 / k 2 , and sin ϕ ( = ( z - x ) / z ) into k sin ϕ , - i tan ϕ , - i k tan ϕ , ( k sin ϕ ) / 1 - k 2 sin 2 ϕ , - i k sin ϕ / 1 - k 2 sin 2 ϕ . … The three changes of parameter of Π ( ϕ , α 2 , k ) in §19.7(iii) are unified in (19.21.12) by way of (19.25.14). … The sign on the right-hand side of (19.25.35) will change whenever one crosses a curve on which ( z ) - e j < 0 , for some j . … The sign on the right-hand side of (19.25.40) will change whenever one crosses a curve on which σ j 2 ( z ) < 0 , for some j . …