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1: 28.5 Second Solutions fe n , ge n
§28.5(i) Definitions
Theorem of Ince (1922)
2: 28.2 Definitions and Basic Properties
If q 0 , then for a given value of ν the corresponding Floquet solution is unique, except for an arbitrary constant factor (Theorem of Ince; see also 28.5(i)). …
3: Errata
  • Paragraph Prime Number Theorem (in §27.12)

    The largest known prime, which is a Mersenne prime, was updated from 2 43 , 112 , 609 - 1 (2009) to 2 82 , 589 , 933 - 1 (2018).

  • Section 1.13

    In Equation (1.13.4), the determinant form of the two-argument Wronskian

    1.13.4 𝒲 { w 1 ( z ) , w 2 ( z ) } = det [ w 1 ( z ) w 2 ( z ) w 1 ( z ) w 2 ( z ) ] = w 1 ( z ) w 2 ( z ) - w 2 ( z ) w 1 ( z )

    was added as an equality. In ¶Wronskian (in §1.13(i)), immediately below Equation (1.13.4), a sentence was added indicating that in general the n -argument Wronskian is given by 𝒲 { w 1 ( z ) , , w n ( z ) } = det [ w k ( j - 1 ) ( z ) ] , where 1 j , k n . Immediately below Equation (1.13.4), a sentence was added giving the definition of the n -argument Wronskian. It is explained just above (1.13.5) that this equation is often referred to as Abel’s identity. Immediately below Equation (1.13.5), a sentence was added explaining how it generalizes for n th-order differential equations. A reference to Ince (1926, §5.2) was added.

  • Equation (33.14.15)
    33.14.15 0 ϕ m , ( r ) ϕ n , ( r ) d r = δ m , n

    The definite integral, originally written as 0 ϕ n , 2 ( r ) d r = 1 , was clarified and rewritten as an orthogonality relation. This follows from (33.14.14) by combining it with Dunkl (2003, Theorem 2.2).