Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9060)

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=-21/4, b_1`>=-11/2

For fixed z and a₁=-21/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.9060.01

Input Form

HypergeometricPFQ[{-(21/4)}, {11/2, -(13/4)}, z] == (-27792237677329125 + 27792237677329125 E^(4 Sqrt[z]) - 55584475354658250 Sqrt[z] - 55584475354658250 E^(4 Sqrt[z]) Sqrt[z] - 45594638770180500 z + 45594638770180500 E^(4 Sqrt[z]) z - 17076643734150000 z^(3/2) - 17076643734150000 E^(4 Sqrt[z]) z^(3/2) - 1138442915610000 z^2 + 1138442915610000 E^(4 Sqrt[z]) z^2 + 728603465990400 z^(5/2) + 728603465990400 E^(4 Sqrt[z]) z^(5/2) - 214709233939200 z^3 + 214709233939200 E^(4 Sqrt[z]) z^3 + 56317176115200 z^(7/2) + 56317176115200 E^(4 Sqrt[z]) z^(7/2) - 14820309504000 z^4 + 14820309504000 E^(4 Sqrt[z]) z^4 + 4118136422400 z^(9/2) + 4118136422400 E^(4 Sqrt[z]) z^(9/2) - 1248725237760 z^5 + 1248725237760 E^(4 Sqrt[z]) z^5 + 425097953280 z^(11/2) + 425097953280 E^(4 Sqrt[z]) z^(11/2) - 167462830080 z^6 + 167462830080 E^(4 Sqrt[z]) z^6 + 79272345600 z^(13/2) + 79272345600 E^(4 Sqrt[z]) z^(13/2) - 47563407360 z^7 + 47563407360 E^(4 Sqrt[z]) z^7 + 39460012032 z^(15/2) + 39460012032 E^(4 Sqrt[z]) z^(15/2) - 53955526656 z^8 + 53955526656 E^(4 Sqrt[z]) z^8 + 219043332096 z^(17/2) + 219043332096 E^(4 Sqrt[z]) z^(17/2) + 1073741824 z^9 - 1073741824 E^(4 Sqrt[z]) z^9 - 4294967296 z^(19/2) - 4294967296 E^(4 Sqrt[z]) z^(19/2) - 268435456 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(35/4) (-819 + 16 z) Erf[Sqrt[2] z^(1/4)] + 268435456 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(35/4) (-819 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z])/(1096646860108800 z^(9/2))

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]