Generalized hypergeometric function 1F2: Specific values (formula 07.22.03.a85q)

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`=1/2

http://functions.wolfram.com/07.22.03.a85q.01

Input Form

HypergeometricPFQ[{-(15/4)}, {1/2, 13/4}, z] == (1/(78517370880 z^(9/4))) ((-4 z^(1/4) (212837625 + 283783500 Sqrt[z] - 356756400 z - 648648000 z^(3/2) - 2595939840 z^2 + 13063403520 z^(5/2) + 1118085120 z^3 - 4688609280 z^(7/2) - 75694080 z^4 + 305922048 z^(9/2) + 1048576 z^5 - 4194304 z^(11/2) + E^(4 Sqrt[z]) (212837625 - 283783500 Sqrt[z] - 356756400 z + 648648000 z^(3/2) - 2595939840 z^2 - 13063403520 z^(5/2) + 1118085120 z^3 + 4688609280 z^(7/2) - 75694080 z^4 - 305922048 z^(9/2) + 1048576 z^5 + 4194304 z^(11/2))) + E^(2 Sqrt[z]) Sqrt[2 Pi] (212837625 - 583783200 z + 7783776000 z^2 - 55351296000 z^3 + 18977587200 z^4 - 1226833920 z^5 + 16777216 z^6) Erf[Sqrt[2] z^(1/4)] + E^(2 Sqrt[z]) Sqrt[2 Pi] (212837625 - 583783200 z + 7783776000 z^2 - 55351296000 z^3 + 18977587200 z^4 - 1226833920 z^5 + 16777216 z^6) 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]