Some families of Weierstrass-type functions and their applications

Chang, Chung-Hau; Srivástava, H. M.; Wu, Tsu-Chen

doi:10.1080/10652460802230546

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The Derivatives Of the Weierstrass-type Functions1

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Cited by 10 publications

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“…Following the earlier investigations by Chang et al ([3] and [4]) (see also Wu et al [21]), the Weierstrasstype functions ℘ 2n are defined by…”

Section: The Derivatives Of the Weierstrass-type Functionsmentioning

confidence: 99%

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A sequence of modular forms associated with higher-order derivatives of Weierstrass-type functions

Aygunes

Şimşek

Srivástava

2016

Filomat

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In this article, we first determine a sequence { f n (τ)} n∈N of modular forms with weight 2 n k + 4(2 n−1 − 1) (n ∈ N; k ∈ N \ {1}; N := {1, 2, 3, • • • }). We then present some applications of this sequence which are related to the Eisenstein series and the cusp forms. We also prove that higher-order derivatives of the Weierstrass type ℘ 2n-functions are related to the above-mentioned sequence { f n (τ)} n∈N of modular forms.

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“…Following the earlier investigations by Chang et al ([3] and [4]) (see also Wu et al [21]), the Weierstrasstype functions ℘ 2n are defined by…”

Section: The Derivatives Of the Weierstrass-type Functionsmentioning

confidence: 99%

“…In Section 2, we shall find it to be convenient to recall a family of Weierstrass-type functions which were introduced and investigated by Chang et al (see, for details, [3] [4]; see also [21]). The above-defined Weierstrass ℘-function ℘(u; w) will then turn out to be a special case of the Weierstrass-type functions.…”

mentioning

confidence: 99%

A sequence of modular forms associated with higher-order derivatives of Weierstrass-type functions

Aygunes

Şimşek

Srivástava

2016

Filomat

View full text Add to dashboard Cite

show abstract

“…An another interesting arithmetical identity (which was stated by Ramanujan) see [23, p. 146], for some analytical proofs of this identity, one may refer to [2, p. 329], [3, p. 136] and [21], also [27] is ; for n ∈ N, we have σ r (k)σ s (n − mk) = Aσ r+s+1 (n) + Bnσ r+s−1 (n) (5) using the theory of modular forms. The (5) holds for every n satisfying some suitable congruences for integers m ≥ 2 and r, s = 1 or 3.…”

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confidence: 99%