A unified presentation of identities involving Weierstrass-type functions and their applications

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

doi:10.1016/j.aml.2010.03.024

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The Derivatives Of the Weierstrass-type Functions1

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Cited by 3 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.…”

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confidence: 99%