Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a8s4)

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=-13/4, b_1`>=-11/2

For fixed z and a₁=-13/4, b_1`=11/2

http://functions.wolfram.com/07.22.03.a8s4.01

Input Form

HypergeometricPFQ[{-(13/4)}, {11/2, 3/4}, z] == (1/(4120022016 z^(9/2))) ((-638512875 + 638512875 E^(4 Sqrt[z]) - 1277025750 Sqrt[z] - 1277025750 E^(4 Sqrt[z]) Sqrt[z] - 899999100 z + 899999100 E^(4 Sqrt[z]) z - 97297200 z^(3/2) - 97297200 E^(4 Sqrt[z]) z^(3/2) + 143292240 z^2 - 143292240 E^(4 Sqrt[z]) z^2 - 37739520 z^(5/2) - 37739520 E^(4 Sqrt[z]) z^(5/2) - 40435200 z^3 + 40435200 E^(4 Sqrt[z]) z^3 + 107827200 z^(7/2) + 107827200 E^(4 Sqrt[z]) z^(7/2) - 251596800 z^4 + 251596800 E^(4 Sqrt[z]) z^4 + 1343619072 z^(9/2) + 1343619072 E^(4 Sqrt[z]) z^(9/2) + 141617664 z^5 - 141617664 E^(4 Sqrt[z]) z^5 - 594462720 z^(11/2) - 594462720 E^(4 Sqrt[z]) z^(11/2) - 9781248 z^6 + 9781248 E^(4 Sqrt[z]) z^6 + 39518208 z^(13/2) + 39518208 E^(4 Sqrt[z]) z^(13/2) + 131072 z^7 - 131072 E^(4 Sqrt[z]) z^7 - 524288 z^(15/2) - 524288 E^(4 Sqrt[z]) z^(15/2) - 128 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-11261835 + 4700592 z - 309504 z^2 + 4096 z^3) Erf[Sqrt[2] z^(1/4)] + 128 E^(2 Sqrt[z]) Sqrt[2 Pi] z^(19/4) (-11261835 + 4700592 z - 309504 z^2 + 4096 z^3) 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]