Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9016)

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`=9/2

http://functions.wolfram.com/07.22.03.9016.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(9/4)}, z] == (1/(4866776006400 z^(7/2))) ((4743512148375 - 4743512148375 E^(4 Sqrt[z]) + 9487024296750 Sqrt[z] + 9487024296750 E^(4 Sqrt[z]) Sqrt[z] + 6599669076000 z - 6599669076000 E^(4 Sqrt[z]) z + 549972423000 z^(3/2) + 549972423000 E^(4 Sqrt[z]) z^(3/2) - 1042053012000 z^2 + 1042053012000 E^(4 Sqrt[z]) z^2 + 555761606400 z^(5/2) + 555761606400 E^(4 Sqrt[z]) z^(5/2) - 247005158400 z^3 + 247005158400 E^(4 Sqrt[z]) z^3 + 108893030400 z^(7/2) + 108893030400 E^(4 Sqrt[z]) z^(7/2) - 51674112000 z^4 + 51674112000 E^(4 Sqrt[z]) z^4 + 28075622400 z^(9/2) + 28075622400 E^(4 Sqrt[z]) z^(9/2) - 18662031360 z^5 + 18662031360 E^(4 Sqrt[z]) z^5 + 16680222720 z^(11/2) + 16680222720 E^(4 Sqrt[z]) z^(11/2) - 24001904640 z^6 + 24001904640 E^(4 Sqrt[z]) z^6 + 100411637760 z^(13/2) + 100411637760 E^(4 Sqrt[z]) z^(13/2) + 1525678080 z^7 - 1525678080 E^(4 Sqrt[z]) z^7 - 6153043968 z^(15/2) - 6153043968 E^(4 Sqrt[z]) z^(15/2) - 16777216 z^8 + 16777216 E^(4 Sqrt[z]) z^8 + 67108864 z^(17/2) + 67108864 E^(4 Sqrt[z]) z^(17/2) + 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (387345 - 23520 z + 256 z^2) Erf[Sqrt[2] z^(1/4)] - 262144 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(27/4) (387345 - 23520 z + 256 z^2) 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]