# 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

... 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

... 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

... 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

... (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

... 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

... 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

... 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

... 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

... 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

... 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

... 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

... 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

... 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

... 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

... (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

... 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

... 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

... 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

... 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

... 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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