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values at infinity

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1: 7.2 Definitions
Values at Infinity
Values at Infinity
2: 6.2 Definitions and Interrelations
Values at Infinity
3: 6.4 Analytic Continuation
Analytic continuation of the principal value of E 1 ( z ) yields a multi-valued function with branch points at z = 0 and z = . …
4: 4.23 Inverse Trigonometric Functions
Table 4.23.1: Inverse trigonometric functions: principal values at 0, ± 1 , ± .
x arcsin x arccos x arctan x arccsc x arcsec x arccot x
5: 12.14 The Function W ( a , x )
W ( a , x ) and W ( a , - x ) form a numerically satisfactory pair of solutions when - < x < .
§12.14(ii) Values at z = 0 and Wronskian
These follow from the contour integrals of §12.5(ii), which are valid for general complex values of the argument z and parameter a . … Then as x
Negative a , - < x <
6: 10.9 Integral Representations
Also, ( t 2 - 1 ) ν - 1 2 is continuous on the path, and takes its principal value at the intersection with the interval ( 1 , ) . …
7: 4.17 Special Values and Limits
§4.17 Special Values and Limits
Table 4.17.1: Trigonometric functions: values at multiples of 1 12 π .
θ sin θ cos θ tan θ csc θ sec θ cot θ
0 0 1 0 1
π / 2 1 0 1 0
8: 4.31 Special Values and Limits
§4.31 Special Values and Limits
Table 4.31.1: Hyperbolic functions: values at multiples of 1 2 π i .
z 0 1 2 π i π i 3 2 π i
tanh z 0 i 0 - i 1
sech z 1 - 1 0
coth z 0 0 1
9: 3.6 Linear Difference Equations
If, as n , the wanted solution w n grows (decays) in magnitude at least as fast as any solution of the corresponding homogeneous equation, then forward (backward) recursion is stable. … The least value of N that satisfies (3.6.9) is found to be 16. … For a difference equation of order k ( 3 ), …Typically k - conditions are prescribed at the beginning of the range, and conditions at the end. …
10: 13.14 Definitions and Basic Properties
In general M κ , μ ( z ) and W κ , μ ( z ) are many-valued functions of z with branch points at z = 0 and z = . …