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11: 33.10 Limiting Forms for Large ρ or Large | η |
§33.10 Limiting Forms for Large ρ or Large | η |
§33.10(i) Large ρ
§33.10(ii) Large Positive η
§33.10(iii) Large Negative η
12: 22.5 Special Values
§22.5(ii) Limiting Values of k
Table 22.5.3: Limiting forms of Jacobian elliptic functions as k 0 .
sn ( z , k ) sin z cd ( z , k ) cos z dc ( z , k ) sec z ns ( z , k ) csc z
Table 22.5.4: Limiting forms of Jacobian elliptic functions as k 1 .
sn ( z , k ) tanh z cd ( z , k ) 1 dc ( z , k ) 1 ns ( z , k ) coth z
13: 10.7 Limiting Forms
§10.7 Limiting Forms
14: 26.9 Integer Partitions: Restricted Number and Part Size
§26.9(iv) Limiting Form
15: 10.28 Wronskians and Cross-Products
16: 20.13 Physical Applications
In the singular limit τ 0 + , the functions θ j ( z | τ ) , j = 1 , 2 , 3 , 4 , become integral kernels of Feynman path integrals (distribution-valued Green’s functions); see Schulman (1981, pp. 194–195). …
17: 13.2 Definitions and Basic Properties
It can be regarded as the limiting form of the hypergeometric differential equation (§15.10(i)) that is obtained on replacing z by z / b , letting b , and subsequently replacing the symbol c by b . … Although M ( a , b , z ) does not exist when b = n , n = 0 , 1 , 2 , , many formulas containing M ( a , b , z ) continue to apply in their limiting form. …
§13.2(iii) Limiting Forms as z 0
§13.2(iv) Limiting Forms as z
18: 26.10 Integer Partitions: Other Restrictions
§26.10(v) Limiting Form
19: 10.24 Functions of Imaginary Order
Y ~ ν ( x ) = 2 / ( π x ) sin ( x 1 4 π ) + O ( x 3 2 ) .
20: 28.12 Definitions and Basic Properties