Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.9024)

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/07.22.03.9024.01

Input Form

HypergeometricPFQ[{-(21/4)}, {9/2, -(1/4)}, z] == (1/(324451733760 z^(7/2))) ((32564156625 - 32564156625 E^(4 Sqrt[z]) + 65128313250 Sqrt[z] + 65128313250 E^(4 Sqrt[z]) Sqrt[z] + 34735100400 z - 34735100400 E^(4 Sqrt[z]) z - 17367550200 z^(3/2) - 17367550200 E^(4 Sqrt[z]) z^(3/2) - 10525788000 z^2 + 10525788000 E^(4 Sqrt[z]) z^2 + 25261891200 z^(5/2) + 25261891200 E^(4 Sqrt[z]) z^(5/2) - 33682521600 z^3 + 33682521600 E^(4 Sqrt[z]) z^3 + 46181560320 z^(7/2) + 46181560320 E^(4 Sqrt[z]) z^(7/2) - 87276994560 z^4 + 87276994560 E^(4 Sqrt[z]) z^4 + 427637145600 z^(9/2) + 427637145600 E^(4 Sqrt[z]) z^(9/2) + 32743327680 z^5 - 32743327680 E^(4 Sqrt[z]) z^5 - 137512569600 z^(11/2) - 137512569600 E^(4 Sqrt[z]) z^(11/2) - 2335656960 z^6 + 2335656960 E^(4 Sqrt[z]) z^6 + 9483694080 z^(13/2) + 9483694080 E^(4 Sqrt[z]) z^(13/2) + 47923200 z^7 - 47923200 E^(4 Sqrt[z]) z^7 - 192479232 z^(15/2) - 192479232 E^(4 Sqrt[z]) z^(15/2) - 262144 z^8 + 262144 E^(4 Sqrt[z]) z^8 + 1048576 z^(17/2) + 1048576 E^(4 Sqrt[z]) z^(17/2) + 16 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (28143325665 - 8701318080 z + 594961920 z^2 - 12042240 z^3 + 65536 z^4) Erf[Sqrt[2] z^(1/4)] - 16 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (28143325665 - 8701318080 z + 594961920 z^2 - 12042240 z^3 + 65536 z^4) Erfi[Sqrt[2] z^(1/4)])/E^(2 Sqrt[z]))

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]