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11: 1.4 Calculus of One Variable
A removable singularity of f ( x ) at x = c occurs when f ( c + ) = f ( c ) but f ( c ) is undefined. … …
12: 4.8 Identities
The restriction on z 1 can be removed when z 2 is an integer.
13: 16.15 Integral Representations and Integrals
16.15.3 F 3 ( α , α ; β , β ; γ ; x , y ) = Γ ( γ ) Γ ( β ) Γ ( β ) Γ ( γ β β ) Δ u β 1 v β 1 ( 1 u v ) γ β β 1 ( 1 u x ) α ( 1 v y ) α d u d v , ( γ β β ) > 0 , β > 0 , β > 0 ,
14: 5.11 Asymptotic Expansions
5.11.3 Γ ( z ) = e z z z ( 2 π z ) 1 / 2 Γ ( z ) e z z z ( 2 π z ) 1 / 2 k = 0 g k z k ,
5.11.14 Γ ( z + a ) Γ ( z + b ) ( z + a + b 1 2 ) a b k = 0 H k ( a , b ) ( z + 1 2 ( a + b 1 ) ) 2 k .
15: 8.12 Uniform Asymptotic Expansions for Large Parameter
The right-hand sides of equations (8.12.9), (8.12.10) have removable singularities at η = 0 , and the Maclaurin series expansion of c k ( η ) is given by … A different type of uniform expansion with coefficients that do not possess a removable singularity at z = a is given by …
16: 3.1 Arithmetics and Error Measures
During the calculations common divisors are removed from the rational numbers, and the final results can be converted to decimal representations of arbitrary length. …
17: 11.6 Asymptotic Expansions
18: 16.5 Integral Representations and Integrals
In (16.5.3) the restriction z < 1 can be removed when p < q . …
19: 18.1 Notation
20: 25.11 Hurwitz Zeta Function
25.11.36Removed because it is just (25.15.1) combined with (25.15.3).