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Haut PDF Finding all hypergeometric solutions of linear differential equations

Haut PDF Finding all hypergeometric solutions of linear differential equations ont été compilés par 123dok FR

Finding all hypergeometric solutions of linear differential equations

Finding all hypergeometric solutions of linear differential equations

... L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignemen[r] ... Voir le document complet

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SOME PROPERTIES OF TWO LINEARLY INDEPENDENT MEROMORPHIC SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS

SOME PROPERTIES OF TWO LINEARLY INDEPENDENT MEROMORPHIC SOLUTIONS OF SECOND ORDER LINEAR DIFFERENTIAL EQUATIONS

... not all vanishing identically such that max { ρ p ( ) ( ) d 1 , ρ p d 2 } < ρ p ( ) B ...meromorphic solutions whose poles are of uniformly bounded multiplicity of ...polynomial of ... Voir le document complet

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Growth of solutions and oscillation of differential polynomials generated by some complex linear differential equations

Growth of solutions and oscillation of differential polynomials generated by some complex linear differential equations

... hypotheses of Theorem ...not all equal to zero with ρ(d j ) < n (j = 0, 1, 2), ϕ(z) is an entire function with finite order such that ψ(z) is not a solution of equation ...solution of ... Voir le document complet

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Growth of certain combinations of entire solutions of higher order linear differential equations

Growth of certain combinations of entire solutions of higher order linear differential equations

... (ii) Let f (z) be an entire function with ρ (f ) = α ≤ ∞, and let L (f) = a k f (k) + a k −1 f (k −1) + · · · + a 0 f, where a 0 , a 1 , · · · , a k are entire functions which are not all equal zero and satisfy b ... Voir le document complet

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On the growth of solutions of some second order linear differential equations with entire coefficients

On the growth of solutions of some second order linear differential equations with entire coefficients

... satisfies σ 2 (f ) 6 σ. Lemma 2.5 ([7]) Let f (z) be a transcendental meromorphic function, and let α > 1 be a given constant. Then there exist a set E 8 ⊂ (1, ∞) with finite logarithmic measure and a constant B > ... Voir le document complet

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On the [p, q]-order of meromorphic solutions of linear differential equations

On the [p, q]-order of meromorphic solutions of linear differential equations

... then all meromorphic solutions f whose poles are of uniformly bounded multiplicities of equation ...purpose of this paper is to consider the growth of meromorphic ... Voir le document complet

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On the hyper-order of solutions of a class of higher order linear differential equations

On the hyper-order of solutions of a class of higher order linear differential equations

... exp {( 1 − ε ) ( 1 − ρ ) δ ( P d , θ ) r n } ≤ 2k. (3.25) This is absurd. Hence σ ( f ) ≥ n. Assume f is a transcendental meromorphic solution whose poles are of uni- formly bounded multiplicity of equation ... Voir le document complet

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Iterated order of solutions of linear differential equations with entire coefficients

Iterated order of solutions of linear differential equations with entire coefficients

... the linear differential equation A n (z) f (n) + A n−1 (z) f (n−1) + ...then all solutions of this equation are entire functions but when A n is a nonconstant entire function, equation ... Voir le document complet

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On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations

On the hyper-order of transcendental meromorphic solutions of certain higher order linear differential equations

... 5 of finite logarithmic measure such that the estimation ...for all z satisfying |z| = r m ∈ E / 5 , r m → +∞ and arg z = θ ∈ [θ r − δ r , θ r + δ r ...for all z satisfying |z| = r sufficiently large ... Voir le document complet

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On the (p, q)-order of solutions of some complex linear differential equations

On the (p, q)-order of solutions of some complex linear differential equations

... A k (z) f (k) + A k−1 (z) f (k−1) + · · · + A 1 (z) f 0 + A 0 (z) f = 0 (1.4) and A k (z) f (k) + A k−1 (z) f (k−1) + · · · + A 1 (z) f 0 + A 0 (z) f = F(z), (1.5) where k ≥ 2, A j (z) ( j = 0, 1, · · · , k) , F(z) are ... Voir le document complet

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Growth of solutions of linear differential equations in the unit disc

Growth of solutions of linear differential equations in the unit disc

... or of finite (iterated) order of growth in the complex plane [7, 14, 15, ...that all solutions of (1.1) are entire functions of finite order if and only if all ... Voir le document complet

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On the order and hyper-order of meromorphic solutions of higher order linear differential equations

On the order and hyper-order of meromorphic solutions of higher order linear differential equations

... Theorem 1.4 Let P j (z) = P n i=0 a i,j z i (j = 0, 1, . . . , k − 1) be noncon- stant polynomials, where a 0,j , a 1,j , . . . , a n,j (j = 0, 1, . . . , k − 1) are com- plex numbers such that a n,j a n,0 6= 0 (j = 1, ... Voir le document complet

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On the hyper order of solutions of a class of higher order linear differential equations

On the hyper order of solutions of a class of higher order linear differential equations

... where (d 5 > 0, d 6 > 0) are some constants. This is a contradiction. Therefore, when max {c 1 , ..., c s−1 } < c 0 , every solution f ≡ 0 of (1.7) has infinite order. Now we prove that ρ 2 (f ) = n. Put ... Voir le document complet

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Some properties of solutions of certain complex linear differential equations with meromorphic doefficients

Some properties of solutions of certain complex linear differential equations with meromorphic doefficients

... not all equal to zero.If f (z) 6≡ 0 is any meromorphic solution of equation ...00 all have infinitely many fixed points and satisfy λ (f − z) = λ  f 0 − z  = λ  f 00 − z  = ∞, (ii) the ... Voir le document complet

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Differential polynomials generated by meromorphic solutions of [p, q]-order to complex linear differential equations

Differential polynomials generated by meromorphic solutions of [p, q]-order to complex linear differential equations

... (i) max{ρ [p,q] (A i ) : i = 1, 2, · · · , k − 1} < ρ [p,q] (A 0 ) = ρ (0 < ρ < +∞) or that (ii) max{ρ [p,q] (A i ) : i = 1, 2, · · · , k − 1} ≤ ρ [p,q] (A 0 ) = ρ (0 < ρ < +∞) and max{τ M,[p,q] (A i ) : ρ ... Voir le document complet

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On the growth of solutions of some non-homogeneous linear differential equations

On the growth of solutions of some non-homogeneous linear differential equations

... has linear measure zero, such that if θ ∈ [0, 2π) \ E 4 , then there is a constant R = R (θ) > 0 such that ...for all z satisfying arg z = θ and |z| ≥ ... Voir le document complet

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Relation between small functions with differential polynomials generated by meromorphic solutions of higher order linear differential equations

Relation between small functions with differential polynomials generated by meromorphic solutions of higher order linear differential equations

... notations of the Nevanlinna value distribution theory of meromorphic functions see [10, ...definition of the iterated order of a meromorphic function, we use the same definition as in [11] , ... Voir le document complet

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Growth of solutions of complex linear differential equations with entire coefficients of finite iterated order

Growth of solutions of complex linear differential equations with entire coefficients of finite iterated order

... Then i λ (f ) = i λ (f ) = i (f ) = p + 1 and λ p+1 (f ) = λ p+1 (f ) = σ p+1 (f ). To avoid some problems caused by the exceptional set, we recall the following lemma. Lemma 2.9 [9] Let g : [0, +∞) → R and h : [0, +∞) → ... Voir le document complet

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Oscillation and fixed points of derivatives of solutions of some linear differential equations

Oscillation and fixed points of derivatives of solutions of some linear differential equations

... function of finite iterated order ρ p (A) = ρ > 0 such that δ (∞, A) = δ > ...(i) all poles of f are of uniformly bounded multiplicity or that (ii) δ (∞, f) > ...0 of (1) ... Voir le document complet

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Infinite order solutions of complex linear differential equations

Infinite order solutions of complex linear differential equations

... growth of solutions of the differential equation f ...for all r 2 E ˇ ; we have min j´jDr jA j ...0 of the above differential equation is of infinite order with ... Voir le document complet

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