Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8414)

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`=7/2

http://functions.wolfram.com/07.22.03.8414.01

Input Form

HypergeometricPFQ[{-(23/4)}, {7/2, 13/4}, z] == (-4 (-12003458206924800 + 13822592969441025 Sqrt[z] - 61592930753577300 z + 41983233407161200 z^(3/2) - 267422080635864000 z^2 - 53834957808065280 z^(5/2) + 240254389299133440 z^3 + 9889622911365120 z^(7/2) - 41135900259041280 z^4 - 564418584576000 z^(9/2) + 2293205987229696 z^5 + 12184156372992 z^(11/2) - 49038716043264 z^6 - 101619597312 z^(13/2) + 407283695616 z^7 + 268435456 z^(15/2) - 1073741824 z^8 + E^(4 Sqrt[z]) (12003458206924800 + 13822592969441025 Sqrt[z] + 61592930753577300 z + 41983233407161200 z^(3/2) + 267422080635864000 z^2 - 53834957808065280 z^(5/2) - 240254389299133440 z^3 + 9889622911365120 z^(7/2) + 41135900259041280 z^4 - 564418584576000 z^(9/2) - 2293205987229696 z^5 + 12184156372992 z^(11/2) + 49038716043264 z^6 - 101619597312 z^(13/2) - 407283695616 z^7 + 268435456 z^(15/2) + 1073741824 z^8)) + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (37829509383290625 + 193687088042448000 z + 1205164103375232000 z^2 - 988852597641216000 z^3 + 166193713889280000 z^4 - 9209002328064000 z^5 + 196458716332032 z^6 - 1629940088832 z^7 + 4294967296 z^8) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(1/4) (37829509383290625 + 193687088042448000 z + 1205164103375232000 z^2 - 988852597641216000 z^3 + 166193713889280000 z^4 - 9209002328064000 z^5 + 196458716332032 z^6 - 1629940088832 z^7 + 4294967296 z^8) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/ (5007404498839142400 z^(5/2))

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]