Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8bu)

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=-15/4, b_1`>=-11/2

For fixed z and a₁=-15/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8bu.01

Input Form

HypergeometricPFQ[{-(15/4)}, {11/2, -(7/4)}, z] == (1/(113700787200 z^(9/2))) ((-1899575803125 + 1899575803125 E^(4 Sqrt[z]) - 3799151606250 Sqrt[z] - 3799151606250 E^(4 Sqrt[z]) Sqrt[z] - 3082740160500 z + 3082740160500 E^(4 Sqrt[z]) z - 1099944846000 z^(3/2) - 1099944846000 E^(4 Sqrt[z]) z^(3/2) - 31426995600 z^2 + 31426995600 E^(4 Sqrt[z]) z^2 + 52929676800 z^(5/2) + 52929676800 E^(4 Sqrt[z]) z^(5/2) - 22313491200 z^3 + 22313491200 E^(4 Sqrt[z]) z^3 + 8302694400 z^(7/2) + 8302694400 E^(4 Sqrt[z]) z^(7/2) - 3193344000 z^4 + 3193344000 E^(4 Sqrt[z]) z^4 + 1362493440 z^(9/2) + 1362493440 E^(4 Sqrt[z]) z^(9/2) - 681246720 z^5 + 681246720 E^(4 Sqrt[z]) z^5 + 424673280 z^(11/2) + 424673280 E^(4 Sqrt[z]) z^(11/2) - 361758720 z^6 + 361758720 E^(4 Sqrt[z]) z^6 + 503316480 z^(13/2) + 503316480 E^(4 Sqrt[z]) z^(13/2) - 2063597568 z^7 + 2063597568 E^(4 Sqrt[z]) z^7 - 16777216 z^(15/2) - 16777216 E^(4 Sqrt[z]) z^(15/2) + 67108864 z^8 - 67108864 E^(4 Sqrt[z]) z^8 + 4194304 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (-495 + 16 z) Erf[Sqrt[2] z^(1/4)] + 4194304 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(29/4) (-495 + 16 z) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

Standard Form

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MathML Form

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Rule 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]