Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8442)

HypergeometricPFQ

$Mathematica Notation$

Hypergeometric Functions

HypergeometricPFQ[{a₁},{b₁,b₂},z]

Specific values

For rational parameters with larger denominators and fixed z

For fixed z and a₁=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=9/2

http://functions.wolfram.com/07.22.03.8442.01

Input Form

HypergeometricPFQ[{-(23/4)}, {9/2, -(7/4)}, z] == (14230536445125 - 14230536445125 E^(4 Sqrt[z]) + 28461072890250 Sqrt[z] + 28461072890250 E^(4 Sqrt[z]) Sqrt[z] + 18431932919400 z - 18431932919400 E^(4 Sqrt[z]) z - 1084231348200 z^(3/2) - 1084231348200 E^(4 Sqrt[z]) z^(3/2) - 4081812134400 z^2 + 4081812134400 E^(4 Sqrt[z]) z^2 + 3401510112000 z^(5/2) + 3401510112000 E^(4 Sqrt[z]) z^(5/2) - 2093236992000 z^3 + 2093236992000 E^(4 Sqrt[z]) z^3 + 1236015728640 z^(7/2) + 1236015728640 E^(4 Sqrt[z]) z^(7/2) - 784114974720 z^4 + 784114974720 E^(4 Sqrt[z]) z^4 + 583536476160 z^(9/2) + 583536476160 E^(4 Sqrt[z]) z^(9/2) - 566018703360 z^5 + 566018703360 E^(4 Sqrt[z]) z^5 + 861685678080 z^(11/2) + 861685678080 E^(4 Sqrt[z]) z^(11/2) - 3728367157248 z^6 + 3728367157248 E^(4 Sqrt[z]) z^6 - 102457737216 z^(13/2) - 102457737216 E^(4 Sqrt[z]) z^(13/2) + 417641791488 z^7 - 417641791488 E^(4 Sqrt[z]) z^7 + 2661285888 z^(15/2) + 2661285888 E^(4 Sqrt[z]) z^(15/2) - 10695475200 z^8 + 10695475200 E^(4 Sqrt[z]) z^8 - 16777216 z^(17/2) - 16777216 E^(4 Sqrt[z]) z^(17/2) + 67108864 z^9 - 67108864 E^(4 Sqrt[z]) z^9 + 16384 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (-232105995 + 25611696 z - 653568 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 16384 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(25/4) (-232105995 + 25611696 z - 653568 z^2 + 4096 z^3) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (28396771603200 z^(7/2))

Standard Form

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MathML Form

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Date Added to functions.wolfram.com (modification date)

2007-05-02

HypergeometricPFQ[{},{},z]
HypergeometricPFQ[{},{b},z]
HypergeometricPFQ[{a},{},z]
HypergeometricPFQ[{a},{b},z]
HypergeometricPFQ[{a₁,a₂},{b₁},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃},{b₁,b₂},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄},{b₁,b₂,b₃},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅},{b₁,b₂,b₃,b₄},z]
HypergeometricPFQ[{a₁,a₂,a₃,a₄,a₅,a₆},{b₁,b₂,b₃,b₄,b₅},z]
HypergeometricPFQ[{a₁,...,a_p},{b₁,...,b_q},z]