By Joel L Malter
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Extra resources for Byzantine numismatic bibliography, 1966-1994
11) ∇ or “del” Vector operator (cf. 21) ∇2 Laplacian (cf. 31) ∼ Asymptotically equal to arg z The argument of the complex number z = x + iy curl or rot Vector operator (cf. 21) div Vector operator (divergence) (cf. 21) F Fourier transform (cf. 21) Fc Fourier cosine transform (cf. 31) Fs Fourier sine transform (cf. 31) grad Vector operator (gradient) (cf. 21) hi and gij Metric coeﬃcients (cf. 51) H Hermitian transpose of a vector or matrix (cf. 123) H(x) = 0 x<0 1 x≥0 Heaviside step function Im z ≡ y The imaginary part of the complex number z = x + iy k The letter k (when not used as an index of summation) denotes a number in the interval [0, 1].
P ; β1 , . . , βq ; z) F p q 1 (α, β; γ; z) = F (α, β; γ; z) F 2 1 (α; γ; z) = Φ(α, γ; z) F 1 1 FΛ (α :β1 , . . , βn ; γ1 , . . . , γn : z1 , . . , zn ) F1 , F2 , F3 , F4 fen (z, q), Fen (z, q) . . Feyn (z, q), Fekn (z, q) . . G g2 , g3 gd x gen (z, q), Gen (z, q) Geyn (z, q), Gekn (z, q) x G m,n p,q a1 ,... ,ap b1 ,... 401 Bessel functions Notation Symbol Meaning The integral part of the real number x (also denoted by [x]) x (b+) (b−) a a Contour integrals; the path of integration starting at the point a extends to the point b (along a straight line unless there is an indication to the contrary), encircles the point b along a small circle in the positive (negative) direction, and returns to the point a, proceeding along the original path in the opposite direction.
2k − 1)! 27958530 . . 590636855 . . (k + 1)! (k + n)! 22389078 . . 57672481 . . (k + 1)! (k + n)! 1 k! = (n + k − 1)! (n − 2) · (n − 1)! kn = Sn , k! 54030 . . (2k)! 2 k=0 ∞ 13 (k + 1)3 = 15e k! 250 Suppose that a sequence of numbers a1 , a2 , . . , ak , . . is given. If the limit lim n→∞ (1 + ak ) k=1 exists, whether ﬁnite or inﬁnite (but of deﬁnite sign), this limit is called the value of the inﬁnite product ∞ (1 + ak ), and we write k=1 ∞ n 1. lim n→∞ (1 + ak ) = k=1 (1 + ak ) k=1 If an inﬁnite product has a ﬁnite nonzero value, it is said to converge.
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