Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.8350)

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=-23/4, b_1`>=-11/2

For fixed z and a₁=-23/4, b_1`=5/2

http://functions.wolfram.com/07.22.03.8350.01

Input Form

HypergeometricPFQ[{-(23/4)}, {5/2, -(3/4)}, z] == (1/(7267806000 z^(3/2))) ((204417675 - 204417675 E^(4 Sqrt[z]) + 408835350 Sqrt[z] + 408835350 E^(4 Sqrt[z]) Sqrt[z] - 908523000 z + 908523000 E^(4 Sqrt[z]) z + 1271743200 z^(3/2) + 1271743200 E^(4 Sqrt[z]) z^(3/2) - 1817424000 z^2 + 1817424000 E^(4 Sqrt[z]) z^2 + 3536225280 z^(5/2) + 3536225280 E^(4 Sqrt[z]) z^(5/2) - 17638871040 z^3 + 17638871040 E^(4 Sqrt[z]) z^3 - 1492285500 z^(7/2) - 1492285500 E^(4 Sqrt[z]) z^(7/2) + 6300262320 z^4 - 6300262320 E^(4 Sqrt[z]) z^4 + 119160000 z^(9/2) + 119160000 E^(4 Sqrt[z]) z^(9/2) - 484621056 z^5 + 484621056 E^(4 Sqrt[z]) z^5 - 2716672 z^(11/2) - 2716672 E^(4 Sqrt[z]) z^(11/2) + 10915840 z^6 - 10915840 E^(4 Sqrt[z]) z^6 + 16384 z^(13/2) + 16384 E^(4 Sqrt[z]) z^(13/2) - 65536 z^7 + 65536 E^(4 Sqrt[z]) z^7 + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-18662576625 + 6387192000 z - 486643200 z^2 + 10928128 z^3 - 65536 z^4) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] z^(13/4) (-18662576625 + 6387192000 z - 486643200 z^2 + 10928128 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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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]