Identities for Generalized Appell Functions and the Blow-up Formula

Appell M.P.: Sur les fonctions doublement périodique de troisième espèce. Annales scientifiques de l’E.N.S. 3(1), 9–42 (1886)

Borwein J., Borwein P.: A cubic counterpart of Jacobi’s identity and the AGM. Trans. Am. Math. Soc. 323(2), 691–701 (1991)

Bringmann K., Manschot J.: Sheaves on $${\mathbb{P}^2}$$ P 2 to a generalization of the Rademacher expansion. Am. J. Math. 135, 1039–1065 (2013)

Bringmann, K., Rolen, L., Zwegers, S.: On the modularity of certain functions from the Gromov–Witten theory of elliptic orbifolds. R. Soc. Open Sci. p. 150310 (2015)

Conway, J.; and Sloane, N.: Sphere Packings, Lattices, and Groups. Springer, New York (1999)

Eichler, M., Zagier, D.: The Theory of Jacobi Forms. Birkhäuser, Boston (1985)

Göttsche L.: Betti numbers of the Hilbert scheme of points on a smooth projective surface. Math. Ann. 286, 193–207 (1990)

Göttsche L.: functions and Hodge numbers of moduli spaces of sheaves on rational surfaces. Commun. Math. Phys. 206, 105–136 (1999)

Ismail, M., Zhang, R.: q-Bessel Functions and Rogers–Ramanujan Type Identities. arXiv:1508.06861 [math.CA]

Kac V.G., Wakimoto M.: Integrable highest weight modules over affine superalgebras and Appell’s function. Commun. Math. Phys. 215, 631–682 (2001)

Kac, V.G., Wakimoto, M.: Representations of Affine Superalgebras and Mock Theta Functions. arXiv:1308.1261 [math.RT]

Li W.P., Qin Z.: On blowup formulae for the S-duality conjecture of Vafa and Witten. Invent. Math. 136, 451–482 (1999)

Manschot J.: Invariants of semi-stable sheaves on rational surfaces. Lett. Math. Phys. 103(8), 895–918 (2013)

Manschot, J.: Sheaves on $${\mathbb{P}^2}$$ P 2 and generalized Appell functions. arXiv:1407.7785 [math.AG]

Raum, M.: H-harmonic Maaß–Jacobi forms of degree 1. Res. Math. Sci. 2(12) (2015)

Schultz, D.: Cubic theta functions. Adv. Math. 248, 618–697 (2013)

Semikhatov A.M., Taormina A., Tipunin I.Y.: Higher level Appell functions, modular transformations, and characters. Commun. Math. Phys. 255, 469–512 (2005)

Vafa C., Witten E.: A strong coupling test of S duality. Nucl. Phys. B 431(1–2), 3–77 (1994)

Yoshioka K.: The Betti numbers of the moduli space of stable sheaves of rank 2 on $${\mathbb{P}^2}$$ P 2 . J. Reine. Angew Math. 453, 193–220 (1994)

Yoshioka K.: Chamber structure of polarizations and the moduli of stable sheaves on a ruled surface. Int. J. Math. 7, 411–431 (1996)

Zwegers, S.P.: Mock Theta Functions. Dissertation, University of Utrecht (2002)

Zwegers, S.P.: Multivariable Appell Functions. preprint (2010)