q-Hypergeometric Proofs of Polynomial Analogues of the Triple Product Identity, Lebesgue?s Identity and Euler?s Pentagonal Number Theorem

q-HYPERGEOMETRIC PROOFS OF POLYNOMIAL ANALOGUES OF THE TRIPLE PRODUCT IDENTITY, LEBESGUE’S IDENTITY AND EULER’S PENTAGONAL NUMBER THEOREM

X iv :m at h/ 02 03 22 9v 1 [ m at h. C O ] 2 2 M ar 2 00 2 2000]Primary 05A19, 33D15 q-HYPERGEOMETRIC PROOFS OF POLYNOMIAL ANALOGUES OF THE TRIPLE PRODUCT IDENTITY, LEBESGUE’S IDENTITY AND EULER’S PENTAGONAL NUMBER THEOREM S. OLE WARNAAR Abstract. We present alternative, q-hypergeometric proofs of some polynomial analogues of classical q-series identities recently discovered by Alladi and Berk...

the crisis of identity in jhumpa lahiris fiction: interpreter of maladies and the namesake

شکل گیری هویت(identity) مقوله مهمی در ادبیات پراکنده مردم(diasporan literature) می باشد. آثار جومپا لاهیری(jhumpa lahiri) ، نویسنده هندی آمریکایی، در سالهای اخیر تحسین منتقدین را به خود معطوف کرده است. وی در این آثار زندگی مهاجران و تلاش آنان برای پیدا کردن جایگاهشان در یک فرهنگ بیگانه را به تصویر کشیده است. این تجربه همواره با احساساتی نظیر دلتنگی برای گذشته، بیگانگی و دوری همراه است. با این ح...

Euler’s Pentagonal Number Theorem and the Rogers-fine Identity

Euler discovered the pentagonal number theorem in 1740 but was not able to prove it until 1750. He sent the proof to Goldbach and published it in a paper that finally appeared in 1760. Moreover, Euler formulated another proof of the pentagonal number in his notebooks theorem around 1750. Euler did not publish this proof or communicate it to his correspondents, probably because of the difficulty...

Bilinear Identity for q - Hypergeometric Integrals

On the q-Analogues of Srivastava's Triple Hypergeometric Functions

We find Euler integral formulas, summation and reduction formulas for q-analogues of Srivastava’s three triple hypergeometric functions. The proofs use q-analogues of Picard’s integral formula for the first Appell function, a summation formula for the first Appell function based on the Bayley–Daum formula, and a general triple series reduction formula of Karlsson. Many of the formulas are purel...