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11: Ingram Olkin
Olkin’s degrees are B. … He also was a Guggenheim, Fulbright, Humboldt, and Lady Davis Fellow, had an honorary degree from De Montfort University, and was awarded the Townsend Harris Medal by the City University of New York. …
12: 14.1 Special Notation
§14.1 Special Notation
x , y , τ real variables.
m , n unless stated otherwise, nonnegative integers, used for order and degree, respectively.
μ , ν general order and degree, respectively.
1 2 + i τ complex degree, τ .
13: 31.8 Solutions via Quadratures
31.8.2 w ± ( 𝐦 ; λ ; z ) = Ψ g , N ( λ , z ) exp ( ± i ν ( λ ) 2 z 0 z t m 1 ( t 1 ) m 2 ( t a ) m 3 d t Ψ g , N ( λ , t ) t ( t 1 ) ( t a ) )
Here Ψ g , N ( λ , z ) is a polynomial of degree g in λ and of degree N = m 0 + m 1 + m 2 + m 3 in z , that is a solution of the third-order differential equation satisfied by a product of any two solutions of Heun’s equation. The degree g is given by
31.8.3 g = 1 2 max ( 2 max 0 k 3 m k , 1 + N ( 1 + ( 1 ) N ) ( 1 2 + min 0 k 3 m k ) ) .
14: 14.31 Other Applications
§14.31(iii) Miscellaneous
Legendre functions P ν ( x ) of complex degree ν appear in the application of complex angular momentum techniques to atomic and molecular scattering (Connor and Mackay (1979)). …
15: 14.11 Derivatives with Respect to Degree or Order
§14.11 Derivatives with Respect to Degree or Order
14.11.3 𝖠 ν μ ( x ) = sin ( ν π ) ( 1 + x 1 x ) μ / 2 k = 0 ( 1 2 1 2 x ) k Γ ( k ν ) Γ ( k + ν + 1 ) k ! Γ ( k μ + 1 ) ( ψ ( k + ν + 1 ) ψ ( k ν ) ) .
16: Bibliography G
  • W. Gautschi (1964a) Algorithm 222: Incomplete beta function ratios. Comm. ACM 7 (3), pp. 143–144.
  • W. Gautschi (1964b) Algorithm 236: Bessel functions of the first kind. Comm. ACM 7 (8), pp. 479–480.
  • W. Gautschi (1969) Algorithm 363: Complex error function. Comm. ACM 12 (11), pp. 635.
  • J. H. Gunn (1967) Algorithm 300: Coulomb wave functions. Comm. ACM 10 (4), pp. 244–245.
  • 17: 14.14 Continued Fractions
    14.14.1 1 2 ( x 2 1 ) 1 / 2 P ν μ ( x ) P ν μ 1 ( x ) = x 0 y 0 + x 1 y 1 + x 2 y 2 + ,
    14.14.3 ( ν μ ) Q ν μ ( x ) Q ν 1 μ ( x ) = x 0 y 0 x 1 y 1 x 2 y 2 , ν μ ,
    18: 30.5 Functions of the Second Kind
    30.5.1 𝖰𝗌 n m ( x , γ 2 ) , n = m , m + 1 , m + 2 , .
    30.5.2 𝖰𝗌 n m ( x , γ 2 ) = ( 1 ) n m + 1 𝖰𝗌 n m ( x , γ 2 ) ,
    30.5.4 𝒲 { 𝖯𝗌 n m ( x , γ 2 ) , 𝖰𝗌 n m ( x , γ 2 ) } = ( n + m ) ! ( 1 x 2 ) ( n m ) ! A n m ( γ 2 ) A n m ( γ 2 ) ( 0 ) ,
    19: George E. Andrews
    He holds honorary degrees from the Universities of Parma, Florida, Waterloo, Illinois, and SASTRA University (India). …
    20: Ranjan Roy
    (1974) degrees in mathematics from the Indian Institute of Technology Kharagpur, Indian Institute of Technology Kanpur, and the State University of New York at Stony Brook, respectively. …