On the Gosper’s q-constant Πq

Bachraoui, Mohamed El

doi:10.1007/s10114-018-8019-4

Cited by 9 publications

(6 citation statements)

References 13 publications

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“…Remark 3. As mentioned in the introduction, El Bachraoui [2] proved that the square of both sides of (L12-2) are equal. Now by Lemma 2.6 we see that (L12-2) holds.…”

Section: Proof Sincementioning

confidence: 92%

“…Remark The identity in part (a) of[2, Theorem 4.1] is the same with (L8-1). The identities in parts (b,c,d) of [2, Theorem 4.1] are incorrect.…”

mentioning

confidence: 92%

“…Earlier than He's work [7], El Bachraoui [2] proved that the square of both sides of (L12-2) are equal. He did not realize that this fact actually proves (L12-2) with few more arguments (see Lemma 2.6 and Remark 3 in this paper).…”

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confidence: 99%

“…El Bachraoui also proved the equivalence of (L12-4) and (L12-5). Furthermore, El Bachraoui reproved (L8-1) (see [2,Theorem 4.1(a)]) and stated some new identities [2,. However, some of his identities are incorrect or contain typos (see Remark 1).…”

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confidence: 99%

“…The identities (L12-10), (L12-11) and (L12-12) are the correct identities corresponding to (b),(c),(d), respectively. We recover these identities by checking the proofs given by El Bachraoui in[2]. (2) Identity (L12-13) is part (a) of [2, Theorem 4.2].…”

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confidence: 99%

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Modular Proofs of Gosper's Identities

Wang¹

2021

Preprint

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We give unified modular proofs to all of Gosper's identities on the qconstant Πq. We also confirm Gosper's observation that for any distinct positive integers n1, • • • , nm with m ≥ 3, Π q n 1 , • • • , Πqnm satisfy a nonzero homogeneous polynomial. Our proofs provide a method to rediscover Gosper's identities. Meanwhile, several results on Πq found by El Bachraoui have been corrected. Furthermore, we illustrate a strategy to construct some of Gosper's identities using hauptmoduls for genus zero congruence subgroups.

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“…Remark 3. As mentioned in the introduction, El Bachraoui [2] proved that the square of both sides of (L12-2) are equal. Now by Lemma 2.6 we see that (L12-2) holds.…”

Section: Proof Sincementioning

confidence: 92%

“…Remark The identity in part (a) of[2, Theorem 4.1] is the same with (L8-1). The identities in parts (b,c,d) of [2, Theorem 4.1] are incorrect.…”

mentioning

confidence: 92%

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confidence: 99%

mentioning

confidence: 99%

mentioning

confidence: 99%

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